[tex]Area\ of\ a\ triangle = 1/2 * base * height\\
height = base + 7cm\\
Area = 60 cm^{2} = 1/2 * base * (base + 7cm)\\
\\
60=\frac{b^{2}+7b}{2}\\
60*2=b^{2}+7b\\
b^{2}+7b-120=0\\\\
Factor:
\\
(b-8)(b+15)\\
b=8\ or\ b=-15\\
Lengths\ cannot\ be\ negative,\ so\ the\ length\ of\ the\ base\ is\ 8.[/tex]
