Question

The height of a right triangle is 5 units more than twice its base. If the area of the triangle is 21 square units, what is its height?

Answer 1

`\displaystyle \\ h = 2b+5 ~~\Longrightarrow~~ 2b = h-5 ~~\Longrightarrow~~ \boxed{b = (h-5)/(2)} \\ \\ A = 21 \\ \\ A=(b * h)/(2)\\\\ 21 = (b * h)/(2)\\\\ 21 = ((h-5)/(2) * h)/(2)\\\\ 42=(h-5)/(2) * h\\\\ 42=(h(h-5))/(2)\\\\ 84=h(h-5) \\ h^2 -5h -84=0 \\ (h+7)(h-12)=0 \\ \Longrightarrow~~h+7=0 ~~or~~h-12 = 0\\ h+7 = 0 ~~\Longrightarrow~~h=-7~~~unacceptable ~~because -7 \ \textless \ 0\\ h-12 = 0 ~~\Longrightarrow~~\boxed{h=12}`