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ISEE Upper Level Quantitative : How to find the area of a rectangle

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Example Question #281 : Geometry

The perimeter of a rectangle is 210 inches. The width of the rectangle is 40% of its length. What is the area of the rectangle?

Possible Answers:

$2,750\textrm{ in}^{2}$

$3,250 \textrm{ in}^{2}$

$3.000 \textrm{ in}^{2}$

$1,750\textrm{ in}^{2}$

$2,250 \textrm{ in}^{2}$

Correct answer:

$2,250 \textrm{ in}^{2}$

Explanation:

If the width of the rectangle is 40% of the length, then

W = 0.40 L .

The perimeter of the rectangle is:

P = 2L + 2W

P = 2L + 2 (0.4L)

P = 2L + 0.8L

P = 2 .8L

The perimeter is 210 inches, so we can solve for the length:

2.8L = 210

$2.8L \div 2.8 = 210 \div 2.8$

L = 75

$W = 0.40 \times 75 = 30$

The length and width of the rectangle are 75 and 30 inches; the area is their product, or

$75\times 30 = 2,250$ square inches.

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Example Question #282 : Geometry

is a positive integer.

Rectangle A has length K + 8 and width K + 4 ; Rectangle B has length K + 10 and length K + 2 . Which is the greater quantity?

(A) The area of Rectangle A

(B) The area of Rectangle B

Possible Answers:

(A) and (B) are equal

It is impossible to determine which is greater from the information given

(A) is greater

(B) is greater

Correct answer:

(A) is greater

Explanation:

This might be easier to solve if you set u = K + 6 .

Then the dimensions of Rectangle A are u + 2 and u - 2 . The area of Rectangle A is their product:

$(u+2) (u - 2) = u ^{2} -4$

The dimensions of Rectangle B are u + 4 and u - 4 . The area of Rectangle B is their product:

$(u+4) (u - 4) = u ^{2} -16$

$u ^{2} - 4 > u ^{2} -16$ regardless of the value of (or, subsequently, ), so Rectangle A has the greater area.

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Example Question #11 : How To Find The Area Of A Rectangle

In Rectangle RECT , $RE = 2 ^{x}$ and $EC = 4 ^{x}$ . Give the area of this rectangle in terms of .

Possible Answers:

$4 ^{x+4}$

$8^{x}$

$4 ^{x+2}$

$6^{x}$

$16^{x}$

Correct answer:

$8^{x}$

Explanation:

The area of a rectangle is the product of its length and its width, which here are $2 ^{x}$ and $4^{x}$ . Mulitply:

$A = 2 ^{x} \cdot 4^{x} = (2 \cdot 4)^{x} = 8^{x}$

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ISEE Upper Level Quantitative : How to find the area of a rectangle

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #281 : Geometry

Example Question #282 : Geometry

Example Question #11 : How To Find The Area Of A Rectangle

All ISEE Upper Level Quantitative Resources

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