Question

the perimeter of an equilateral triangle is 18 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. (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 $(x + 8)$ inches.

Step2: Calculate the perimeters.

The perimeter of the square is $P_{square}=4x$ inches, and the perimeter of the equilateral triangle is $P_{triangle}=3(x + 8)$ inches.

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

We know that the perimeter of the equilateral triangle is 18 inches more than the perimeter of the square. So, $3(x + 8)=4x+18$.

Step4: Expand and solve the equation.

Expand the left - hand side: $3x+24 = 4x+18$.
Subtract $3x$ from both sides: $24=x + 18$.
Subtract 18 from both sides: $x = 6$.

Step5: Find the side - length of the triangle.

The side - length of the triangle is $x + 8$. Substitute $x = 6$ into it, we get $6+8=14$ inches.

Answer:

14