When the length of each side of a square is decreased by 20cm, its area is decreased by 5600cm^2. How do you find the length of a side of the square before the decrease?

Aug 10, 2016

Write a systems of equations. Let $l$ be the side length of the square and $A$ the area. So, we can say:

${l}^{2} = A$

${\left(l - 20\right)}^{2} = A - 5600$

We are looking to find $l$. I think in this case substitution would be easiest.

${\left(l - 20\right)}^{2} = {l}^{2} - 5600$

${l}^{2} - 40 l + 400 = {l}^{2} - 5600$

${l}^{2} - {l}^{2} - 40 l + 400 + 5600 = 0$

$- 40 l + 6000 = 0$

$- 40 l = - 6000$

$l = 150$

Hence, the initial length was $150$ centimetres.

Hopefully this helps!