Question

The area of a square is numerically 45 more than the perimeter. find the length of the side

Answer 1

Area of square = l²
Perimeter of square = 4l

According to the question,

`l^2 = 45 + 4l \\\\ l^2 - 4l - 45 = 0 \\\\ l^2 -9l+5l-45=0 \\\\ l(l-9)+5(l-9) =0 \\\\(l-9)(l+5)=0`

Using zero product property,

Either,

`l-9 = 0 \\ ~~~~~~l = 9`

Or,

`l+5=0 \\ ~~~~~~l=-5`

Since length can't be negative, the length is 9