Chapter 3.4, Problem 17WE

To determine

The value of n that makes the triangle equilateral.

Answer to Problem 17WE

For n=5 triangle is equilateral

Explanation of Solution

Given:

Sides of triangle are given, $4n,2n+10,7n-15$

For a triangle to be equilateral all the sides of the triangle are equal.

Therefore,

  $\begin{array}{l}4n=2n+10\\ 2n=10\\ n=5\end{array}$

Now, substitute the value of n in all the sides of triangle.

For side 1,

  $\begin{array}{l}4n=4\times 5\\ =20\end{array}$

For side 2,

  $\begin{array}{l}2n+10\\ =2\times 5+10\\ =20\end{array}$

For side 3,

  $\begin{array}{l}7n-15\\ =7\times 5-15\\ =20\end{array}$

Therefore, for n = 5 all the sides are equal and so triangle is equilateral.