Which of the following triangles is a multiple of the triangle with sides measuring x, x – 5, and x + 5, when x is greater than 0?

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Accepted Answer

The hypotenuse of the given triangle is x + 5, since x cannot be 0 or negative (the side of a triangle cannot be 0 or negative); therefore, x + 5 > x > x – 5. Using the Pythagorean theorem: (x) 2 + (x – 5) 2 = (x + 5) 2 x 2 + x 2 – 10x + 25 = x 2 + 10x + 25 2x 2 – 10x + 25 = x 2 + 10x + 25 x 2 – 20x = 0, x(x – 20) = 0, and x = 20, since x cannot be 0. Therefore, the sides of the triangle measure 20, 20 – 5 = 15, and 20 + 5 = 25. The sides of the triangle, 15, 20, 25, are a multiple of the triangle with sides 3, 4, 5, since 3(5) = 15, 4(5) = 20, and 5(5) = 25.

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