### All Basic Geometry Resources

## Example Questions

### Example Question #1 : How To Find The Length Of The Side Of A Rectangle

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

**Possible Answers:**

11

3

5

7

17

**Correct answer:**

7

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

Simplify

Solve for S

### Example Question #2 : How To Find The Length Of The Side Of A Rectangle

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.

**Possible Answers:**

**Correct 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 .

### Example Question #1 : How To Find The Length Of The Side Of A Rectangle

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 ?

**Possible Answers:**

**Correct 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:

### Example Question #3 : How To Find The Length Of The Side Of A Rectangle

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

**Possible Answers:**

**Correct 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.

### Example Question #2 : How To Find The Length Of The Side Of A Rectangle

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

**Possible Answers:**

**Correct answer:**

If we call the width of this rectangle , then its length can be restated as, 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:

### Example Question #2 : How To Find The Length Of The Side Of A Rectangle

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?

**Possible Answers:**

w = 2l – 2

w = ½ l – 2

w = ½ l + 2

w = 2l + 2

**Correct answer:**

w = ½ l + 2

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

### Example Question #3 : How To Find The Length Of The Side Of A Rectangle

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,?

**Possible Answers:**

w = 3l – 2

w = 6l +2

w = 3l + 2

w = 1/3l +2

**Correct answer:**

w = 3l + 2

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

### Example Question #3 : How To Find The Length Of The Side Of A Rectangle

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)?

**Possible Answers:**

48

60

81

32

36

**Correct answer:**

48

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.

### Example Question #4 : How To Find The Length Of The Side Of A Rectangle

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

**Possible Answers:**

**Correct answer:**

Recall how to find the perimeter of a rectangle.

We can then manipulate this equation to find the width.

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

### Example Question #1 : How To Find The Length Of The Side Of A Rectangle

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

**Possible Answers:**

**Correct answer:**

Recall how to find the perimeter of a rectangle.

We can then manipulate this equation to find the width.

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

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