the congruent sides of an isosceles triangle are each 1 unit longer than the length of the shortest side of…

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

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

Answer

Explanation:

Step1: Let the length of the shortest side of the triangle be $x$.

The congruent sides of the isosceles - triangle are $x + 1$ each. The perimeter of the isosceles triangle $P_{triangle}=x+(x + 1)+(x + 1)=3x + 2$.

Step2: The side - length of the square is $x-2$.

The perimeter of the square $P_{square}=4(x - 2)=4x-8$.

Step3: Set the perimeters equal.

Since $P_{triangle}=P_{square}$, we have the equation $3x + 2=4x-8$.

Step4: Solve the equation for $x$.

Subtract $3x$ from both sides: $3x+2-3x=4x - 8-3x$, which gives $2=x - 8$. Then add 8 to both sides: $2 + 8=x-8 + 8$, so $x = 10$.

Answer:

10