Question

Find the dimensions of a triangle whose width is four more than six times its height and has an area of 208 square inches.

Short answer

Therefore, the Dimension of a triangle ,width is $52inches$and Height is 8 inches.

Step-by-step solution

Given information

The given statement width is four more than six times its height .

Area of a triangle is 208 square inches.

Simplification of the equation

h = the height of a triangle.

4 + $6h$= the width

208 = Area of a triangle.

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

208 = $\frac{1}{2}\times \left(4+6h\right)\left(h\right)$

Simplify

localid="1648572463497" $$\begin{gathered} 416=\left(4+6h\right)\left(h\right) \\ 416=4h+6h^2 \\ Take2asacommon \\ 3h^2+2h-208=0 \\ a=3,b=2andc=-208 \\ U\sin gquadraticformula \\ h=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ h=\frac{-2\pm \sqrt{2^2+4\left(3\right)\left(208\right)}}{2\left(3\right)} \\ h=\frac{-2+50}{6}or\frac{-2-50}{6} \\ h=\frac{48}{6},\frac{-52}{6} \\ h=8,-8.6\left(notpossible\right) \\ b=4+6\left(8\right) \\ =52 \end{gathered}$$