Question

the perimeter of an equilateral triangle is 13 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

Explanation:

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

The side - length of the equilateral triangle is $x + 7$ inches.

Step2: Calculate the perimeters.

The perimeter of the square is $P_{square}=4x$ inches. The perimeter of the equilateral triangle is $P_{triangle}=3(x + 7)$ inches.

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

We know that the perimeter of the equilateral triangle is 13 inches more than the perimeter of the square. So, $3(x + 7)=4x+13$.

Step4: Expand the left - hand side of the equation.

$3x+21 = 4x+13$.

Step5: Solve for $x$.

Subtract $3x$ from both sides: $21=x + 13$. Then subtract 13 from both sides: $x=21 - 13=8$.

Step6: Find the side - length of the triangle.

The side - length of the triangle is $x + 7$. Substitute $x = 8$ into it, we get $8+7=15$ inches.

Answer:

15