Question

A rectangle has an area of 48 square feet and a perimeter of 32 feet. Which of the following could be its dimensions?

Answer 1

area=l*w
perimeter=2(l+w)

l*w=48

2(l+w)=32
l+w=32/2
l+w=16
l=16-w

now substitute l in (l*w=48)

(16-w)*w=48
16w-w^2=48
w^2-16w+48=0
w^2-12w-4w+48=0
w(w-12)-4(w-12)=0
(w-12)(w-4)=0
w=12,w=4

so dimensions are 12 and 4