Question

the perimeter of an equilateral triangle is 17 inches more than the perimeter of a square, and the side of the triangle is 8 inches longer than the side of the square. find the side of the triangle. (note: an equilateral triangle has three sides the same length.) the side of the triangle is

Explanation:

Step1: Define variables

Let the side length of the square be \(x\) inches. Then the side length of the equilateral triangle is \(x + 8\) inches.
The perimeter of the square is \(P_{square}=4x\) inches, and the perimeter of the equilateral triangle is \(P_{triangle}=3(x + 8)\) inches.

Step2: Set up the equation

Since the perimeter of the equilateral triangle is 17 inches more than the perimeter of the square, we have the equation:
\(3(x + 8)=4x+17\)

Step3: Solve the equation

Expand the left - hand side: \(3x+24 = 4x + 17\)
Subtract \(3x\) from both sides: \(24=x + 17\)
Subtract 17 from both sides: \(x=24 - 17=7\)

Step4: Find the side length of the triangle

The side length of the triangle is \(x + 8\). Substitute \(x = 7\) into \(x + 8\), we get \(7+8 = 15\)

Answer:

15