Question

If the sides of a square are lengthened by 6cm, the area becomes 144 cm^2. Find the length of the original square.

Answer 1

There's the long way to do this (probably the way they want you to work it) and the short way.

I'll show you the long way first then come back with the short way.

Let x = length of the original square. Then x + 6 is the length of the new square.

A= l^2 ofr a square, s\[144=(x+6)^{2}=x^{2}+12x+36\]\[x^{2}+12x-108=0\]
Solve this for x (using factoring or quadratic formula) and discard the negative value.

Answer 2

THe short way is to say that if the new square has an area of 144cm^2, then the length of the new square is 12cm. THis is 6cm longer than the original, so the original is 6cm.