It’s length is? It’s width is?

Question

A rectangle has an area of 171 cm^2 and a perimeter of 56 cm. What are its dimensions?

Answer 1

A = LW= 171

P = 2L +2W = 56

L+W = 56/2 = 28

L = 28-W

(28-W)W = 171

W^2 -28 -171 = 0

factor to get (W-19)(W-9)=0 or

complete the square

W^2 -28W = -171

W^2 -28W +14^2 = -171+14^2

W -14 = sqr(-171+196) = sqr25= 5

W=14+ or - 5 = 9 or 19 cm

L = 28-W =28-9 or 28-19 = 19 or 9 cm

the dimensions are 9 cm by 19 cm

9x19 =171

2(9+19)=56