The congruent sides of an isosceles triangle are each 1 unit longer than the length of the shortest side of the triangle. The perimeter of the triangle is the same as the perimeter of a square whose side length is 2 units shorter than the length of the shortest side of the triangle. What is the length of the shortest side of the triangle? ____ units

1 answer

Let x be the length of the shortest side of the triangle.

Since the congruent sides of the isosceles triangle are each 1 unit longer than the shortest side, the other two sides are x + 1.

The perimeter of the isosceles triangle is then x + x + 1 + x + 1 = 3x + 2.

The perimeter of the square is (x - 2) * 4 = 4x - 8.

Since the perimeters of the triangle and square are equal, we have:

3x + 2 = 4x - 8
2 = x - 8
x = 10

Therefore, the length of the shortest side of the triangle is 10 units.