Question

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 1

Answer:

10 units

Step-by-step explanation:

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.

Answer 2

A = 10

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