Chapter 12.6, Problem 5P

To determine

To find: the altitude of a triangle.

Answer to Problem 5P

The altitude of a triangle will be $9cm$ .

Explanation of Solution

Given information:

The area of a triangle is $162c{m}^2$ and the base is fourth times of its altitude.

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 base is fourth times of altitude.

Therefore $b=4h$ 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 $\frac{1}{2}*4h*h=162\Rightarrow h^2=81\Rightarrow h=\pm 9.$

The altitude $h$ will be $+9$ because height cannot be negative value.

Therefore the altitude of a triangle will be $9cm$ .