A rectangle and square have the same area, what are the dimensions of the rectangle?

Question

The width of the rectangle is 48 cm less than the side of the square and the length of the rectangle is 128 cm more than twice the side of the square. What are the dimensions of the​ rectangle?

Answer 1

w = s-48

L = 128 +2s

wL = s^2

(s-48)(2s + 128) = s^2

2s^2 +32s - 48(128) = s^2

s^2 + 32s -6144 = 0

s=64

w = 64-48 = 16 cm

L = 128+2(64) = 256 cm

both have area = 4096 cm^2

= 64^2 = 16(256)