How to find the length of the side of a rectangle - Geometry

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Question

The width, in cm, of a rectangular fence is 2 more than half its length, in cm. Which of the following gives the width, w cm, in terms of length, l cm, of the rectangular fence?

Answer

To find the width, we must take half of the length, which means we must divide the length by 2. Then we must take 2 more than that number, which means we must add 2 to the number. Combining these, we get:

w = ½ l + 2

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Question

The width of a rectangle is 2 inches longer than 3 times its length. Which of the following equations gives the width, w, of the rectangle in terms of its length, l,?

Answer

The width equals 3 times the length, so 3l, plus an additional two inches, so + 2, = 3l + 2

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Question

Your dad shows you a rectangular scale drawing of your house. The drawing is 6 inches by 8 inches. You're trying to figure out the actual length of the shorter side of the house. If you know the actual length of the longer side is 64 feet, what is the actual length of the shorter side of the house (in feet)?

Answer

We can solve this by setting up a proportion and solving for x,the length of the shorter side of the house. If the drawing is scale and is 6 : 8, then the actual house is x : 64. Then we can cross multiply so that 384 = 8_x_. We then divide by 8 to get x = 48.

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Question

A rectangle four and a half times as long as it is wide has perimeter of 272 centimeters. To the nearest tenth of a centimeter, how wide is it?

Answer

If we call the width of this rectangle , then its length can be restated as $L=4\frac{1}{2}w$ , or, equivalently, .

The perimeter can then be written as:

Since the perimeter of the rectangle is 272 cm, we can set up the following equation:

$w=\frac{272}{11}=24.7$

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Question

The rectangle below has a perimeter of 54. Find the lengths of the unknown side. That is, find S.

Answer

For a rectangle, its perimeter is the sum of all for sides. We can write

Simplify

Solve for S

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Question

Given a rectangle with a length units longer than its width and an area of square units, find the length of the rectangle's shortest side.

Answer

The given rectangle has a length that is units longer than its width. This can be expressed in the following equation, where is the length and is the width of the rectangle.

Since the area of the rectangle is equal to its length multiplied by its width (), and the area of the rectangle is given, the following equation must be true.

Replacing in this equation with its value stated in the first equation results in the following.

Distribute the variable into the parentheses.

Factor the polynomial.

and are both solutions for this equation, but is not valid as a width for a rectangle. The width of the rectangle is units, which is the shorter side since the length is units longer .

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Question

There is a regtangular fence surrounding a park. The perimeter of the fence is . What is the width of the fence if the length is ?

Answer

The formula for the perimeter of a rectangle is:

, where represents the length and represents the width.

We know the perimeter of the rectange is and the length is . Plugging these values into the equation, we get:

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Question

A rectangle has a perimiter of 36 inches and a length of 12 inches. What is the width of the rectangle in inches?

Answer

To find the width, multiply the length that you have been given by 2, and subtract the result from the perimeter. You now have the total length for the remaining 2 sides. This number divided by 2 is the width.

$36-(12\cdot 2)=12$

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Question

If the perimeter of a rectangle is , and the length of the rectangle is , what is the width of the rectangle?

Answer

Recall how to find the perimeter of a rectangle.

$\text{Perimeter}=2(\text{length}+\text{width})$

We can then manipulate this equation to find the width.

$\text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\text{width}=\frac{\text{Perimeter}}{2}-\text{length}$

Now, plug in the information given by the question to find the width.

$\text{width}=\frac{40}{2}-12=20-12=8$

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Question

If the perimeter of a rectangle is and the length of the rectangle is , what is the width of the rectangle?

Answer

Recall how to find the perimeter of a rectangle.

$\text{Perimeter}=2(\text{length}+\text{width})$

We can then manipulate this equation to find the width.

$\text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\text{width}=\frac{\text{Perimeter}}{2}-\text{length}$

Now, plug in the information given by the question to find the width.

$\text{width}=\frac{14}{2}-5=7-5=2$

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Question

If the perimeter of a rectangle is and the length of the rectangle is , what is the width of the rectangle?

Answer

Recall how to find the perimeter of a rectangle.

$\text{Perimeter}=2(\text{length}+\text{width})$

We can then manipulate this equation to find the width.

$\text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\text{width}=\frac{\text{Perimeter}}{2}-\text{length}$

Now, plug in the information given by the question to find the width.

$\text{width}=\frac{18}{2}-3=9-3=6$

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Question

If the perimeter of a rectangle is , and the length of the rectangle is , what is the width of the rectangle?

Answer

Recall how to find the perimeter of a rectangle.

$\text{Perimeter}=2(\text{length}+\text{width})$

We can then manipulate this equation to find the width.

$\text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\text{width}=\frac{\text{Perimeter}}{2}-\text{length}$

Now, plug in the information given by the question to find the width.

$\text{width}=\frac{20}{2}-9=10-9=1$

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Question

If the perimeter of the rectangle is , and the length of the rectangle is , what is the width of the rectangle?

Answer

Recall how to find the perimeter of a rectangle.

$\text{Perimeter}=2(\text{length}+\text{width})$

We can then manipulate this equation to find the width.

$\text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\text{width}=\frac{\text{Perimeter}}{2}-\text{length}$

Now, plug in the information given by the question to find the width.

$\text{width}=\frac{54}{2}-12=27-12=15$

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Question

If the perimeter of a rectangle is , and the length of the rectangle is , what is the width of the rectangle?

Answer

Recall how to find the perimeter of a rectangle.

$\text{Perimeter}=2(\text{length}+\text{width})$

We can then manipulate this equation to find the width.

$\text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\text{width}=\frac{\text{Perimeter}}{2}-\text{length}$

Now, plug in the information given by the question to find the width.

$\text{width}=\frac{22}{2}-5=11-5=6$

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Question

If the perimeter of the rectangle is , and the width of the rectangle is , what is the length of the rectangle?

Answer

Recall how to find the perimeter of a rectangle.

$\text{Perimeter}=2(\text{length}+\text{width})$

We can then manipulate this equation to find the length.

$\text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\text{length}=\frac{\text{Perimeter}}{2}-\text{width}$

Now, plug in the information given by the question to find the length.

$\text{length}=\frac{24}{2}-10=12-10=2$

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Question

If the perimeter of a rectangle is , and the width of the rectangle is , what is the length of the rectangle?

Answer

Recall how to find the perimeter of a rectangle.

$\text{Perimeter}=2(\text{length}+\text{width})$

We can then manipulate this equation to find the length.

$\text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\text{length}=\frac{\text{Perimeter}}{2}-\text{width}$

Now, plug in the information given by the question to find the length.

$\text{length}=\frac{200}{2}-54=100-54=46$

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Question

If the perimeter of the rectangle is , and the width of the rectangle is , what is the length of the rectangle?

Answer

Recall how to find the perimeter of a rectangle.

$\text{Perimeter}=2(\text{length}+\text{width})$

We can then manipulate this equation to find the length.

$\text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\text{length}=\frac{\text{Perimeter}}{2}-\text{width}$

Now, plug in the information given by the question to find the length.

$\text{length}=\frac{56}{2}-12=28-12=16$

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Question

If the perimeter of a rectangle is , and the width of the rectangle is , what is the length of the rectangle?

Answer

Recall how to find the perimeter of a rectangle.

$\text{Perimeter}=2(\text{length}+\text{width})$

We can then manipulate this equation to find the length.

$\text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\text{length}=\frac{\text{Perimeter}}{2}-\text{width}$

Now, plug in the information given by the question to find the length.

$\text{length}=\frac{64}{2}-17=32-17=15$

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Question

If the perimeter of a rectangle is , and the width of the perimeter is , what is the length of the rectangle?

Answer

Recall how to find the perimeter of a rectangle.

$\text{Perimeter}=2(\text{length}+\text{width})$

We can then manipulate this equation to find the length.

$\text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\text{length}=\frac{\text{Perimeter}}{2}-\text{width}$

Now, plug in the information given by the question to find the length.

$\text{length}=\frac{66}{2}-15=33-15=18$

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Question

If the perimeter of a rectangle is , and the width of the rectangle is , what is the length of the rectangle?

Answer

Recall how to find the perimeter of a rectangle.

$\text{Perimeter}=2(\text{length}+\text{width})$

We can then manipulate this equation to find the length.

$\text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\text{length}=\frac{\text{Perimeter}}{2}-\text{width}$

Now, plug in the information given by the question to find the length.

$\text{length}=\frac{96}{2}-46=48-46=2$

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