Chapter 12, Problem 18CR

To determine

To find: The possible length of the base of an isosceles triangle with perimeter 36 and one of the sides as 10.

Answer to Problem 18CR

The possible lengths of the base are 10 and 13.

Explanation of Solution

Given Information:

Perimeter of a triangle = 36

One side of a triangle $\left(a\right)=6$

Formula used:

Perimeter of a triangle $=a+b+c$

Where $a,b\text{and}c$ are the sides of a triangle

Calculation:

Let $a,b\text{and}c$ be the three sides of an isosceles triangle

There are two possibilities:

i.

Let $a\text{and}c$ be the equal sides and $b$ be the base

As $a=10\Rightarrow c=10$

We know that, perimeter of a triangle $\left(P\right)=a+b+c$

Perimeter is given as 36

  $\begin{array}{l}\therefore 36=10+b+10\\ \therefore b=16\end{array}$

ii.

Let $b\text{and}c$ are the equal sides such that $b$ is the base

We know that, perimeter of a triangle $\left(P\right)=a+b+c$

As $a=10$ and perimeter is given as 36

  $\begin{array}{l}\therefore 36=10+b+b\\ \therefore 2b=26\\ \therefore b=13\end{array}$

Hence, the possible lengths of the base of an isosceles triangle are 10 and 13.