Question

the side of a triangle with 3 equal sides is s8 inches shorter than the side of a square. The perimeter of the square is 46 inches more than the perimeter of the triangle. Find the length of a side of the square.

Answer 1

Side of the square is 22 inches

Explanation:

We know the side a triangle (with 3 equal sides) is 8 inches shorter then the square length of a side or s-8 where s is the side length of the square. So the triangle has side lengths s-8 which when added together give the perimeter p = 3(s-8) = 3s-24.

Now the square has side length s and 4s = P, its perimeter. We also know that P (perimeter of the square) is 46 inches more than the triangle p perimeter. This means P=46+p.

P=46+p

4s = 46+p Substitute P=4s.

4s=46+3s-24 Substitute p=3s-24.

4s = 3s + 22 Solve for s.

4s-3s = 22

s=22