Question

The width of a rectangle is 3 inches less than its length. The area of the rectangle is 340 square inches. What are the length and width of the rectangle?

Answer 1

A = WL
A = 340
W = L - 3

340 = (L-3)(L)
340 = L^2 - 3L
L^2 - 3L - 340 = 0
L = 20

W = l - 3
W = 20 - 3
W = 17

so the length is 20 inches and the width is 17 inches

Answer 2

The length and width of the rectangle are 20 inches and 17 inches .

Explanation:

Formula

Area of a rectangle = Length × Breadth

As given

The width of a rectangle is 3 inches less than its length. The area of the rectangle is 340 square inches.

Let us assume that the length is denoted by l.

Thus

Breadth = l - 3

Put in the above formula

340 = l × (l - 3)

340 = l² - 3l

l² - 3l - 340 = 0

l² - 20l + 17l - 340 = 0

l(l-20) + 17 (l-20) = 0

(l - 20) ( l+ 17) = 0

l = 20

l = -17 (This valueof length is neglected because length cannot be negative.)

As l = 20 inches

Breadth = 20 - 3

= 17 inches

Therefore the length and width of the rectangle are 20 inches and 17 inches .