The congruent sides of an isosceles triangle are 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 2units shorter than the length of the shortest side of the triangle. what is the length of the shortest side of the triangle?

Let S=shortest side of the isosceles triangle.
Then length of the congruent sides are both S+1 units.
The perimeter is therefore the sum of all three sides
= S+(S+1)+(S+1)
=3S+2

Side length of square = S-2
Perimeter of square = 4(S-2) = 4S-8

Since the perimeter of square is the same as perimeter of isosceles triangle, we write
4S-8=3S+2
Isolate S and solve
4S-3S=2+8
S=10

Ans. the shortest length of the isosceles triangle is 10 units.