Question

a rectangle has a perimeter of 46cm and an area of 120cm squared. find its dimensions by writing an equation and using the quadratic formula to solve it. Thanks!

Answer 1

Let length = l , width = b
Perimeter = 2 (l +b)
46= 2 (l +b)
(l + b) = 23

l*b = 120

So l + 120/l = 23
l^2 + 120 - 23l = 0
l^2 -15l + 8l + 120 = 0
(l-8) (l - 15) =
l = 8 or 15
i.e if l =8, w=15
and if l = 15, w = 8