Question

When the length of each side of a square is increased by 5 cm, its area is increased by 895 cm2. Find the length of a side before the increase.

The length of a side before the increase is...

Answer 1

Explanation:

Increasing the side length by 5 is represented as s + 5. To get the area of a square we multiply side times side:
`(s+5)^2=s^2+10s+25`

The area of a square is s². If we are increasing this area s² by 895, then to represent this we have s² + 895.

Put that together into an equation:

`s^2+10s+25=s^2+895` and simplify to

10s = 870 so

s = 87

Let's check that. The area before the addition to the side is 87*87 = 7569; the area after the addition of 5 cm is 92*92 = 8464. The difference is

8464 - 7569 = 895 so we did good!