Question

A rectangular play area is twice as long as it is wide. If you increase the length by 4m and decrease the width by 3m, the new area will be 532m². Determine the dimensions of the original rectangle ​

Answer 1

length = 34 m , width = 17 m

Explanation:

let the width be w then length l = 2w

increasing l by 4 = 2w + 4

decreasing width by 3 = w - 3

then

(2w + 4)(w - 3) = 532 ← expand left side using FOIL

2w² - 2w - 12 = 532 ( subtract 532 from both sides )

2w² - 2w - 544 = 0 ( divide through by 2 )

w² - w - 272 = 0 ← in standard form

(w + 16)(w - 17) = 0 ← in factored form

equate each factor to zero and solve for w

w + 16 = 0 ⇒ w = - 16

w - 17 = 0 ⇒ w = 17

However , w > 0 then w = 17 and 2w = 2 × 17 = 34

original dimensions are

length = 34 m and width = 17 m