Chapter 12.6, Problem 6P

To determine

To find: the base of a triangle.

Answer to Problem 6P

The base of a triangle will be $12cm$ .

Explanation of Solution

Given information:

The area of a triangle is $42c{m}^2$ and the altitude is $5m$ less than its base.

Formula:

The area of triangle is $\frac{1}{2}*b*h$ Where $b$ is base and $h$ is altitude.

Calculation:

Consider the altitude of a triangle be $h$ and base of triangle be $b$ .

Then as mentioned above that the altitude is $5m$ less than its base.

Therefore $h=b-5$ Where $b$ is base and $h$ is altitude.

Recall that area of triangle is $\frac{1}{2}*b*h$ Where $b$ is base and $h$ is altitude.

Therefore area of triangle will be

  $\begin{array}{l}b\left(b-5\right)=84\Rightarrow b^2-5b-84=0\Rightarrow b^2-12b+7b-84=0\\ \Rightarrow b\left(b-12\right)+7\left(b-12\right)=0\Rightarrow b=12,-7.\end{array}$

The base $b$ will be $12$ because base cannot be negative value.

Therefore the base of a triangle will be $12cm$ .