Rectangles

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ISEE Upper Level Quantitative Reasoning › Rectangles

Questions 1 - 10

Your geometry book has a rectangular front cover which is 12 inches by 8 inches.

What is the area of your book cover?

Explanation

Your geometry book has a rectangular front cover which is 12 inches by 8 inches.

What is the area of your book cover?

To find the area of a rectangle, use the following formula:

$A_{rectangle}=l*w$

Plug in our knowns and solve:

Your geometry book has a rectangular front cover which is 12 inches by 8 inches.

What is the area of your book cover?

Explanation

Your geometry book has a rectangular front cover which is 12 inches by 8 inches.

What is the area of your book cover?

To find the area of a rectangle, use the following formula:

$A_{rectangle}=l*w$

Plug in our knowns and solve:

Your geometry book has a rectangular front cover which is 12 inches by 8 inches.

What is the perimeter of your book cover?

Explanation

Your geometry book has a rectangular front cover which is 12 inches by 8 inches.

What is the perimeter of your book cover?

Perimeter is the distance around the outside of a shape.

Perimeter of a rectangle can be found via the following:

$P_{rectangle}=2l+2w$

Plug in our length and width to find our answer:

Find the area of a rectangle with a width of 8cm and a length that is four times the width.

$256\text{cm}^2$

$128\text{cm}^2$

$32\text{cm}^2$

$96\text{cm}^2$

$80\text{cm}^2$

Explanation

To find the area of a rectangle, we will use the following formula:

$A = l \cdot w$

where l is the length and w is the width of the rectangle.

Now, we know the width of the rectangle is 8cm. We also know the length of the rectangle is four times the width. Therefore, the length of the rectangle is 32cm.

Knowing this, we will substitute into the formula. We get

$A = 32\text{cm} \cdot 8\text{cm}$

$A = 256\text{cm}^2$

Your geometry book has a rectangular front cover which is 12 inches by 8 inches.

What is the perimeter of your book cover?

Explanation

Your geometry book has a rectangular front cover which is 12 inches by 8 inches.

What is the perimeter of your book cover?

Perimeter is the distance around the outside of a shape.

Perimeter of a rectangle can be found via the following:

$P_{rectangle}=2l+2w$

Plug in our length and width to find our answer:

Find the area of a rectangle with a width of 8cm and a length that is four times the width.

$256\text{cm}^2$

$128\text{cm}^2$

$32\text{cm}^2$

$96\text{cm}^2$

$80\text{cm}^2$

Explanation

To find the area of a rectangle, we will use the following formula:

$A = l \cdot w$

where l is the length and w is the width of the rectangle.

Now, we know the width of the rectangle is 8cm. We also know the length of the rectangle is four times the width. Therefore, the length of the rectangle is 32cm.

Knowing this, we will substitute into the formula. We get

$A = 32\text{cm} \cdot 8\text{cm}$

$A = 256\text{cm}^2$

The perimeter of a rectangle is 70; its width is . Which of the following expressions is equal to the length of the rectangle?

$\frac{70}{t+16}$

$\frac{54}{t }$

Explanation

Let be the length. The perimeter of the rectangle is .

Replace and solve for :

$2L + 2 \left ( t+16 \right ) = 70$

$2L \div 2 =\left ( 38 -2t \right ) \div 2$

The area of a rectangle is 40; its width is . Which of the following expressions is equal to the length of the rectangle?

$\frac{40}{s + 5}$

$\frac{35}{s}$

Explanation

Let be the length. The area of the rectangle is . Replace and solve for :

$L \left ( s+5 \right ) = 40$

$L \left ( s+5 \right ) \div \left ( s+5 \right ) = 40 \div \left ( s+5 \right )$

$L = \frac{40}{s + 5}$

You are designing a poster to put on the front of your refrigerator. If the refrigerator door is 2 feet wide by 4.5 feet tall, what is the area of the largest poster you could fit on the door?

Explanation

You are designing a poster to put on the front of your refrigerator. If the refrigerator door is 2 feet wide by 4.5 feet tall, what is the area of the largest poster you could fit on the door?

We need to find the area of a shape. Given the context of a refrigerator door and a poster, we can assume that the poster will be a rectangle. To find the area of a rectangle, we need to multiply length and width.