The congruent sides of an isosceles triangle are each 1 unit longer than the length of the shortest side of the triangle. The pe
rimeter 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
Represent the length of the shortest side of the triangle by x. Then the sum of the lengths of the other two sides is 2(x + 1), and the perimeter of the triangle is thus x + 2(x + 1), or 3x + 2.
Represent the side length of the square by x - 2. Then the perimeter of the square is 2(x - 2) + 2(x - 2) = 4(x - 2) = 4x - 8, and this perimeter matches that of the triangle:
4x - 8 = 3x + 2, or
x = 10
The length of the shortest side of the triangle is 10 units.
