### All ISEE Upper Level Quantitative Resources

## Example Questions

### 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:**

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

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:**

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