Question

the perimeter of an equilateral triangle is 15 inches more than the perimeter of a square, and the side of the triangle is 7 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 blank with a dropdown

Explanation:

Step1: Define variables

Let the side length of the square be \( x \) inches. Then the side length of the triangle is \( x + 7 \) inches.

Step2: Write perimeter formulas

Perimeter of square: \( 4x \)
Perimeter of equilateral triangle: \( 3(x + 7) \)

Step3: Set up equation

Given that the perimeter of the triangle is 15 inches more than the perimeter of the square:
\( 3(x + 7)=4x + 15 \)

Step4: Solve for \( x \)

Expand left side: \( 3x+21 = 4x + 15 \)
Subtract \( 3x \) from both sides: \( 21=x + 15 \)
Subtract 15 from both sides: \( x = 6 \)

Step5: Find triangle's side

Side of triangle: \( x + 7=6 + 7 = 13 \)

Answer:

13 inches