Question

the length of each side of an equilateral triangle is increased by 5 inches, so the perimeter is now 60 inches. write and solve an equation to find the original length of each side of the equilateral triangle. (example 8)
equation:
solution:

Explanation:

Step1: Define variable

Let \( x \) be the original length of each side (in inches) of the equilateral triangle. After increasing each side by 5 inches, the new length of each side is \( x + 5 \) inches. Since an equilateral triangle has 3 equal sides, the perimeter (sum of all sides) is \( 3(x + 5) \) inches, and we know this perimeter is 60 inches. So the equation is \( 3(x + 5)=60 \).

Step2: Solve the equation

First, divide both sides of the equation \( 3(x + 5)=60 \) by 3: \( \frac{3(x + 5)}{3}=\frac{60}{3} \), which simplifies to \( x + 5 = 20 \). Then, subtract 5 from both sides: \( x+5 - 5=20 - 5 \), so \( x = 15 \).

Answer:

Equation: \( 3(x + 5)=60 \)
Solution: \( x = 15 \)