Question

finding a missing dimension
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

Explanation:

Step1: Define variable for shortest side

Let $x$ = length of the triangle's shortest side (in units).

Step2: Express congruent sides length

Each congruent side = $x + 1$

Step3: Calculate triangle perimeter

Perimeter of triangle = $x + 2(x + 1) = x + 2x + 2 = 3x + 2$

Step4: Calculate square side & perimeter

Square side length = $x - 2$, so square perimeter = $4(x - 2) = 4x - 8$

Step5: Set perimeters equal & solve

Set triangle perimeter = square perimeter:
$$3x + 2 = 4x - 8$$
Subtract $3x$ from both sides:
$$2 = x - 8$$
Add 8 to both sides:
$$x = 10$$

Answer:

10 units