the perimeter and area of a rectangle are 48 cm and 140cm^2 respectively. Find the length and width of the rectangle

Answer 1

lw = 140
2l + 2w = 48
l + w = 24
l = 24-w

in lw = 140
w(24-w) = 140
-w^2 + 24w - 140 = 0
w^2 - 24w + 140 = 0
(w-10)(w - 14) = 0
w = 10 or w = 14

if w=10, l= 140/10 = 14
if w = 14, l = 140/14 = 10
we call these symmetric roots

the rectangle is 10 cm by 14 cm