Question

Which is best represent the area of a triangle of a height of x+7 and a base of 2x+12

a. 3x+19
b. 3x^2+84
c. x^2+13x+42
d. 2x^2+26x+84

Answer 1

`\textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ h=x+7\\ b=2x+12 \end{cases}\implies A=\cfrac{1}{2}(2x+12)(x+7) \\\\\\ A=\cfrac{1}{2}\underset{\stackrel{\uparrow \qquad }{\textit{common factoring}}}{2(x+6)(x+7)}\implies A=(x+6)(x+7)\implies A=\stackrel{\mathbb{F~O~I~L}}{x^2+13x+42}`