Question

7 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 5) equation: solution:

Explanation:

Step1: Define variable

Let \( x \) be the original length of each side of the equilateral triangle. After increasing each side by 5 inches, the new length of each side is \( x + 5 \).

Step2: Write perimeter equation

Since an equilateral triangle has 3 equal sides, the perimeter \( P \) is given by \( P = 3\times(\text{length of one side}) \). The new perimeter is 60 inches, so the equation is \( 3(x + 5)=60 \).

Step3: Solve the equation

First, divide both sides by 3: \( x + 5=\frac{60}{3}=20 \). Then, subtract 5 from both sides: \( x = 20 - 5 = 15 \).

Answer:

Equation: \( 3(x + 5) = 60 \)
Solution: \( x = 15 \) (the original length of each side is 15 inches)