Question

the perimeter of an equilateral triangle is 3 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. (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 perimeter of the square is $4x$ inches.

Step2: Let the side - length of the equilateral triangle be $y$ inches.

The perimeter of the equilateral triangle is $3y$ inches.

Step3: Set up equations based on given information.

We know that $y=x + 4$ and $3y=4x + 3$.

Step4: Substitute $y=x + 4$ into $3y=4x + 3$.

$3(x + 4)=4x+3$.
Expand the left - hand side: $3x+12 = 4x + 3$.

Step5: Solve for $x$.

Subtract $3x$ from both sides: $12=x + 3$.
Subtract 3 from both sides: $x = 9$ inches.

Step6: Find the side - length of the triangle.

Since $y=x + 4$, substitute $x = 9$ into this equation. Then $y=9 + 4=13$ inches.

Answer:

13 inches