Chapter 4.8, Problem 12P

To determine

To find the height and the base of the side of the tent.

Answer to Problem 12P

The value of base and height of the tent is $9ft$ and $12ft$ .

Explanation of Solution

Given information:Tent shape whose like an isosceles triangle whose area is $54f{t}^2$ and whose base is 6ft shorter than twice its height.

Calculation: The height and the base of the tent is obtained as,

Let, $x$ is height of triangle, $2x-6$ is base of triangle.

The area of triangle = ½ base times height

  $\begin{array}{l}\frac{1}{2}x\left(2x-6\right)=54\\ x^2-3x=54\\ x^2-3x-54=0\\ x^2+6x-9x-54=0\\ x\left(x+6\right)-9\left(x+6\right)=0\\ \left(x+6\right)\left(x-9\right)=0\\ x=9,-6\end{array}$

Ignore negative value.

  $x=9$ is height of triangle.

  $2x-6=2\cdot 9-6=18-6=12$ is base of triangle.

Hence, the value of base and height of the tent is $9ft$ and $12ft$ .