Question

Which quadratic equation below could be used to represent the following situation?

The Cameron's have a triangular baseball pennant hanging from a flagpole in their yard. The pennant has an area of 50 ft
. The height of the triangle is 20 less than 6 times the length of its base. What equation will describe the area of the pennant?

Answer 1

Check the picture below.

`\textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh ~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ b=x\\ h=6x-20\\ A=50 \end{cases}\implies 50=\cfrac{1}{2}(x)(6x-20) \\\\\\ 50=\cfrac{6x^2-20x}{2}\implies \boxed{50=3x^2-10x}`