A Guide to the GRE/Rectangles

= Rectangles =

The area of a rectangle equals length multiplied by width.

Area = 450

Rectangle questions usually involve algebra and a quadratic equation.

For example, if the length of a rectangle is twice its width, and the rectangle's area is 98, what is the width of the rectangle?

Let w equal width and l equal length.

w(l) = 98	Set up the formula.

w(2w) = 98	Substitute 2l for

$$2w^2 = 98$$	Expand the parentheses.

$$w^2 = 49$$	Divide both sides by 2.

w = 7		Take the square root of both sides.

The width of the rectangle is 7 (and the length is 14).

Practice
1. A rectangle has an area of 132 and its length is 1 greater than its width. What are the dimensions of the rectangle?

2. A rectangle's area would increase by 90 if its length were extended by 18. What is the rectangle's width?

Answers to Practice Questions
1. 11 and 12

The formula for a rectangle's area is length multiplied by width. Thus, this problem can be solved with algebra and factoring. Let l equal the length and w equal the width.

$$l(w) = 132$$		Take the initial equation.

$$(w + 1)(w) = 132$$		Substitute the length in terms of the width.

$$w^2 + w = 132$$			Expand the parentheses.

$$w^2 + w - 132 = 0$$		Subtract 132 from both sides.

$$(w + ?)(w + ?) = 0$$		Break the expression into factors. What two numbers multiply to -132 and add to 1?

$$(w + 12)(w - 11) = 0$$		Factor the equation. w equals 11 or -12. Since the width is not negative, it equals 11.

Using the width, the length can be easily determined by adding 1.

2. 5

Since area of a rectangle is length multiplied by width, the width equals the amount of extension increase - 90 - divided by the increase in length, which is 18. The width is thus 5.