Question

If a triangle that has an area of 110 square feet has a height that is two feet less than twice the width ,what are its dimensions .

Short answer

The Height of a triangle is 22 feet and width of a triangle is 11 feet.

Step-by-step solution

Given information

The given statement is ,feet has a height that is two feet less than twice the width

Area of a triangle is 110 square feet.

Simplification of the equation 

feet = $2b-2$

width = b

Area of a triangle is 110.

Area of a triangle =$\frac{1}{2}\times b\times h$

role="math" localid="1648574441164" $$\begin{gathered} 110=\frac{1}{2}\times \left(2b-2\right)\left(b\right) \\ Simplify \\ 110=\left(b-1\right)\left(b\right) \\ 110=b^2-b \\ {b}^2-b-110=0 \\ x=1,y=-1,z=-110 \\ b=\frac{-y\pm \sqrt{y^2-4xz}}{2x} \\ b=\frac{-\left(-1\right)\pm \sqrt{-1^2-4\left(1\right)}\left(-110\right)}{2} \\ b=\frac{1\pm \sqrt{1+440}}{2} \\ b=\frac{1+21}{2},\frac{1-21}{2} \\ b=11,-10\left(notpossible\right) \\ Heightis22feet. \\ Widthis11feet. \end{gathered}$$