Question

1. The length and width of a certain rectangle with an area of 12 units² can be expressed as x + 2 and
x + 3 respectively. What is the value of x? NOTE: only an algebraic solution will earn credit.

Answer 1

$~~~~(x+2)(x+3) = 12\\\\\implies x^2+3x+2x+6 -12=0\\ \\\implies x^2 +5x -6 = 0\\\\\implies x^2 +6x-x-6 = 0\\\\\implies x(x+6) -(x+6) =0\\\\\implies (x+6)(x-1)=0\\\\\implies x=1~~~~~~~~~;[x\neq -6~ \text{because length cannot be negative.}}]$