Question

A square is altered so that one dimension is increased by 5 meters and the other dimension is increased by 3 meters. If the area of the resulting rectangle is 99 square meters, find the area of the original square.

Answer 1

The area of the original square is
`36\ m^(2)`

Explanation:

Let

x------> the length side of the original square

we know that

`99=(x+5)(x+3)\\ \\99=x^(2) +3x+5x+15\\ \\x^(2) +8x+15-99=0\\ \\ x^(2) +8x-84=0`

Solve the quadratic equation by graphing

The solution is
`x=6\ m`

see the attached figure

The area of the original square is

`A=6^(2)=36\ m^(2)`