Question

The dimensions of a rectangular garden were 5m by 12m. Each dimensions was increased by the same amount. the garden has an area of 120m. Find the dimensions of the new garden .

Answer 1

Let's say, the amount that each side was increased was "a"
so, it was 5 wide and 12 long, now it's 5+a wide and 12+a long

we know the area is 120, so whatever "a" is, we know that

(5+a)(12+a) = 120

so   $\bf (5+a)(12+a) = 120\implies 60+17a+a^2=120 \\\\\\ a^2+\underline{17} a\underline{-60}=0\qquad \qquad \begin{cases} 20\cdot -3\implies \underline{-60}\\\\ 20-3\implies \underline{17} \end{cases}$

use those factors, solve for "a"