Question

the perimeter of an equilateral triangle is 6 inches more than the perimeter of a square, and the side of the triangle is 4 inches longer than the side of the square. find the side of the triangle. (an equilateral triangle has three sides the same length.) the side of the triangle is □

Explanation:

Step1: Let the side - length of the square be $x$ inches.

The side - length of the equilateral triangle is $x + 4$ inches.

Step2: Calculate the perimeters.

The perimeter of the square is $4x$ inches, and the perimeter of the equilateral triangle is $3(x + 4)$ inches.

Step3: Set up the equation based on the given relationship.

We know that the perimeter of the equilateral triangle is 6 inches more than the perimeter of the square. So, $3(x + 4)=4x + 6$.

Step4: Expand and solve the equation.

Expand the left - hand side: $3x+12 = 4x + 6$.
Subtract $3x$ from both sides: $12=x + 6$.
Subtract 6 from both sides: $x = 6$.

Step5: Find the side - length of the triangle.

Since the side - length of the triangle is $x + 4$, substituting $x = 6$ gives $6+4=10$ inches.

Answer:

10 inches