Chapter 4.1, Problem 60HP

To determine

To calculate:

Perimeter of the equilateral triangle.

Answer to Problem 60HP

Perimeter of the equilateral triangle is $69$ units.

Explanation of Solution

Given information:

Side of equilateral triangle: $5x+3$ and $7x-5$

Calculations:

It is given that triangle is equilateral, the sides are equal.

By solving, $5x+3$ equal to $7x-5$

  $5x+3=7x-5$

Add $-3-7x$ to each side

  $5x+3-3-7x=7x-5-3-7x$

Simplify

  $-2x=-8$

Multiply each side of $-2x=-8$ by $-\frac{1}{2}$

  $x=-8\left(-\frac{1}{2}\right)$

Find the value of one side length

  $\begin{array}{l}5x+3\\ =5\left(4\right)+3\\ =20+3\\ =23\end{array}$

Since all the sides are congruent, the perimeter of the triangle is $3\left(23\right)=69$ units.