# A Guide to the GRE/Rectangles

# Rectangles[edit]

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

Expand the parentheses.

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[edit]

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[edit]

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.

Take the initial equation.

Substitute the length in terms of the width.

Expand the parentheses.

Subtract 132 from both sides.

Break the expression into factors. What two numbers multiply to -132 and add to 1?

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.