A rectangle & a square both have a width of x, but the rectangle’s length is (x+6). Together their areas equal 176m^2. What are the dimensions of both ?
The area of the square is
$\displaystyle A_s=x^2$
The area of the rectangle is
$\displaystyle A_r=x(x+6)=x^2+6x$
And we know that there total area is
$\displaystyle A_s+A_r=176$
$\displaystyle x^2+x^2+6x=176 \iff 2(x^2-3x-88)=0 \iff 2(x+11)(x-8)=0$
So we reject the negative solution (why?)
and get $\displaystyle x=8$