Question

Given the area and Perimeter, find the length and width
A= 32 square cm
P= 24 cm

Answer 1

length is 8 and width is 4

or width is 8 and length is 4

Explanation:

given length is l and width is w

then l x w = 32 and 2(l + w) = 24

2(l + w) = 24

l + w = 12

l = 12 - w

Substitute

w(12 - w) = 32

-w^2 + 12w - 32 = 0

w^2 - 12w + 32 = 0

Using quadratic equation ax^2 + bx + c = 0

x = [-b ± √(b^2 - 4ac)] / (2a)

x = [-(-12) ± √(-12^2 - 4(1)(32)] / (2(1))

x = [12 ± √(144 - 128] / 2

x = [12 ± √16] / 2

x = [12 ± 4] / 2

x = [12 + 4] / 2 = 16/2 = 8

x = [12 - 4] / 2 = 8/2 = 4