Question

The lengths of sides of a triangle are $4n,2n+10$and $7n-15$. Is there a value of n that makes the triangle equilateral? Explain.

Short answer

The value of n that makes the triangle equilateral is 5.

Step-by-step solution

. Apply the definition of an equilateral triangle.

An equilateral triangle is a triangle in which all the three sides have the same length.

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

– Description of a step.

Divide each side of the obtained equation in step 1 by to find the value of n.

$\begin{array}{c}\frac{2n}{2}=\frac{10}{2}\\ n=5\end{array}$

Step 3. Description of a step.

Substitute 5 for n into 4n to find the length of first side.

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

Step 4. Description of a step.

Substitute 5 for n into$2n+10$ to find the length of second side.

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

Step 5. Description of a step.

Substitute 5 for n into$7n-15$ to find the length of third side.

$\begin{array}{c}7n-15=7\times 5-15\\ =35-15\\ =20\end{array}$