Question

Originally a rectangle was twice as long as it was wide. When 4 m were added to its length and and 3 m subtracted

from its width, the resulting rectangle has an area of 600 m². Find the dimensions of the new rectangle.

Answer 1

Explanation:

Original rectangle

L = 2*w

w = w

New rectangle

2w + 4

w - 3

Area New rectangle

(2w + 4)(w - 3) = 600 Remove the brackets

2w^2 - 6w + 4w - 12 = 600 Combine the left

2w^2 - 2w - 12 = 600 Subtract 600 from both sides

2w^2 - 2w - 600 - 12 = 0 Combine

2w^2 - 2w - 612 = 0 This factors.

(w- 18)(w + 17) = 0

w + 17 will produce nothing useful. What is - 17 m ? Can you measure it?

w = 18

check

Original Triangle

w = 18

L = 36

Derived Triangle

L = 36 + 4 = 40

w = 18 - 3 = 15

LW = 600

Answer

• L = 40
• W = 15