The perimeter of an equilateral triangle is 7 inches more than the perimeter of a square, and the side of the triangle is 5 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 $$ \square $$ $$ \square $$ Heln me solve this View an example Get more held Clear all Check answer

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Let the side of the square be $$ s $$ and the side of the triangle be $$ t $$.

1. The triangle’s side is given to be 5 inches longer than the square’s side:
   $$
   t = s + 5
   $$

2. The perimeter of the triangle is 7 inches more than the perimeter of the square. Since an equilateral triangle has 3 equal sides and a square has 4 equal sides, we have:
   $$
   3t = 4s + 7
   $$

3. Substitute $$ t = s + 5 $$ into the perimeter equation:
   $$
   3(s + 5) = 4s + 7
   $$

4. Expand the left side:
   $$
   3s + 15 = 4s + 7
   $$

5. Solve for $$ s $$ by subtracting $$ 3s $$ from both sides:
   $$
   15 = s + 7
   $$

6. Subtract 7 from both sides:
   $$
   s = 8
   $$

7. Now, find $$ t $$ using $$ t = s + 5 $$:
   $$
   t = 8 + 5 = 13
   $$

Thus, the side of the triangle is $$ \boxed{13} $$.
The side of the triangle is 13 inches.

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