Question

the perimeter of an equilateral triangle is 7 inches more than the perimeter of a square, and the side of the triangle is 5 inches longer than the side of the square. find the side of the triangle. (hint: an equilateral triangle has three sides the same length.) the side of the triangle is

Explanation:

Step1: Let side of square be \(x\) inches.

Side of equilateral triangle is \(x + 5\) inches.

Step2: Express perimeters.

Perimeter of square is \(4x\) inches, perimeter of equilateral triangle is \(3(x + 5)\) inches.

Step3: Set up equation.

We know \(3(x + 5)=4x + 7\).
Expand left - hand side: \(3x+15 = 4x + 7\).

Step4: Solve for \(x\).

Subtract \(3x\) from both sides: \(15=x + 7\).
Subtract 7 from both sides: \(x = 8\).

Step5: Find side of triangle.

Side of triangle is \(x + 5\), substituting \(x = 8\), we get \(8 + 5=13\) inches.

Answer:

13