Chapter 4.8, Problem 10P

To determine

To find the height of the triangle .

Answer to Problem 10P

The height of the triangle is 10cm.

Explanation of Solution

Given information: Height of the triangle is $7cm$ greater than the length of its base. And its area is $15c{m}^2$ .

Calculation: The height of the triangle is obtained as,

Let, Base = $x$ , Height = $x+7$

Area of triangle is =1/2 base times height.

  $\begin{array}{l}\frac{1}{2}x\left(x+7\right)=15\\ x\left(x+7\right)=30\\ x^2+7x-30=0\\ x^2-3x+10x-30=0\\ x\left(x-3\right)+10\left(x-3\right)=0\\ \left(x-3\right)\left(x+10\right)=0\\ x=3,-10\end{array}$

Ignore negative value.

  $x=3$ is base of triangle.

  $x+7=3+7=10$ is the height of the triangle.

Here, the height of the triangle is 10cm.

Using pytagorean theorem.

  $\begin{array}{l}{x}^2+{\left(x+3\right)}^2={15}^2\\ x^2+x^2+9+6x=225\\ 2x^2+6x+9-225=0\\ 2x^2+6x-216=0\\ x^2+3x-108=0\\ x^2+12x-9x-108=0\\ x\left(x+12\right)-9\left(x+12\right)=0\\ \left(x+12\right)\left(x-9\right)=0\\ x=-12,9\end{array}$

Ignore the negative value.

Hence, 9 ft far is the foot ladder from the bottom of the wall.