A shed has dimensions of 12m in length and 5 m in width. Both the length and width are increased by the same amount in order to increase the floor area by more than double the original area. What is the amount of the increase in length?

Question

(Ok so this is the question, Im thinking that the answer is 24 but my teacher is giving a bunch of marks if I get it right, now I'm thinking it can't be that easy and there must be more to it right? Please help me)

Answer 1

original floor area = 12*5 = 60 m^2
let new length be 12+x
let new width be 5+x
(12+x)(5+x) = 120 , (double the original area)
60 + 17x + x^2 = 120
x^2 + 17x - 60 = 0
(x - 3)(x + 20) = 0
x = 3 or x = -20 , but we can't have a negative side, so

x = 3

check:
new length = 12+3 = 15
new width = 5 + 3 = 8
new area = 15*8 = 120 , which is double the original 60
YEAHH