Chapter 11, Problem 5MCQ

To determine

To find: The base and height of the triangle.

Answer to Problem 5MCQ

The base and height of the triangle are 11 inches and 19 inches respectively.

Explanation of Solution

Given information:

Height of the triangle is 8 inches more that its base, $h=b+8\text{ in}\text{.}$.

Area of the triangle, $A=104.5\text{ in}{\text{.}}^2$ .

Formula used:

Area of the triangle, $A=\frac{1}{2}bh$ ; where b is the base and h is the height.

Calculation:

Calculate the base of the triangle by substituting the given values in the area formula as follows:

  $\begin{array}{c}104.5=\frac{1}{2}b\left(b+8\right)\\ 209=b^2+8b\\ b^2+8b-209=0\end{array}$

Factorize the quadratic equation in b as follow:

  $\begin{array}{c}{b}^2+8b-209=0\\ b^2+19b-11b-209=0\\ b\left(b+19\right)-11\left(b+19\right)=0\\ \left(b-11\right)\left(b+19\right)=0\end{array}$

On solving for b, the values of b are found to be $11\text{ and}-19$ .

The base of a triangle cannot be a negative value.

Hence, the base of the triangle is $b=11\text{ in}\text{.}$ .

Since, given $h=b+8\text{ in}\text{.}$

Now, compute the height of the triangle as follows:

  $\begin{array}{c}h=11+8\\ \text{=19}\end{array}$

Thus, the height of the triangle is $h=19\text{ in}\text{.}$ .

Therefore, the base and height of the triangle are 11 inches and 19 inches respectively.