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

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

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Example Questions

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Example Question #281 : Plane 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:

Correct answer:

Explanation:

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

.

The perimeter of the rectangle is:

 

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

 

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

 square inches.

Example Question #282 : Plane Geometry

 is a positive integer. 

Rectangle A has length  and width ; Rectangle B has length  and length . Which is the greater quantity?

(A) The area of Rectangle A

(B) The area of Rectangle B

Possible Answers:

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

(A) is greater

(A) and (B) are equal

(B) is greater

Correct answer:

(A) is greater

Explanation:

This might be easier to solve if you set .

Then the dimensions of Rectangle A are  and . The area of Rectangle A is their product:

 

The dimensions of Rectangle B are  and .  The area of Rectangle B is their product:

 

 regardless of the value of  (or, subsequently, ), so Rectangle A has the greater area.

Example Question #13 : How To Find The Area Of A Rectangle

In Rectangle  and . Give the area of this rectangle in terms of .

Possible Answers:

Correct answer:

Explanation:

The area of a rectangle is the product of its length and its width, which here are  and . Mulitply:

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