Question

The base of a triangle is 7cm greater than height.the area is 60cm. what is heigh and base

Answer 1

`\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ b=\stackrel{\textit{7 more than the \underline{h}}}{h+7}\\ A=60 \end{cases}\implies 60=\cfrac{1}{2}(h+7)h\implies 120=h^2+7h \\\\\\ 0=h^2+7h-120\implies 0=(h+15)(h-8)\implies h= \begin{cases} -15\\ \boxed{8} \end{cases} \\\\\\ b=h+7\implies \boxed{b=15}`

we cannot use -15 for h, because it's a height, and therefore it cannot be negative.