Question

The length of a rectangle is 5cm more than the width. The area is 24cm^2. What is the length and width?

Answer 1

...x= width

x+5 = length

A = 24 cm²

x(x+5)=24

x²+5x-24=0

Δ = b²-4ac = 5²-4(1*-24)= 121

Δ is strictly positive, the equation x²+5x−24=0 admits two solutions

(-b-√Δ)/2a =(-5-11)/2= -8

(-b+√Δ)/2a=(-5+11)/2 = 3

a length is never negative, we keep the positive value, i.e. 3

x=3

x= width = 3cm

x+5 = length = 3+5 =8cm