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?
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Explanation:

Step1: Define variable for short side

Let $x$ = length of shortest triangle side.

Step2: Label congruent sides

Congruent sides: $x + 1$

Step3: Find square side length

Square side: $x - 2$

Step4: Set perimeter equality

Triangle perimeter = Square perimeter
$x + 2(x+1) = 4(x-2)$

Step5: Simplify and solve for $x$

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

Answer:

10 units