Question

A square has side lengths of (5x + 6) unitd. An equilateral triangle has side lengths of (7x + 1) units. The square and the triangle have the same perimeter. What is the value of x? Solve algebraically.

Answer 1

x = 3/16

Explanation:

Square's perimeter must equal triangle's perimeter. Using the given formulas for the two different perimeters, we obtain the equation

5x + 6 = 3(7x + 1), where 5x + 7 includes all four sides of the square and

7x + 1 includes all three sides of the triangle.

Performing the indicated multiplication, we get 5x + 6 = 21x + 3.

Combining like terms results in 3 = 16x.

Solving this last equation for x, we get x = 3/16.