The sides of a right-angled triangle are in the ratio x:(x-1):(x-18). What is the perimeter of the triangle?

Explanation

Assuming the sides are x, x-1, x-18 where x is the hypotenuse, applying the Pythagorean theorem gives (x-18)^2 + (x-1)^2 = x^2. Expanding gives x^2 - 36x + 324 + x^2 - 2x + 1 = x^2, which simplifies to x^2 - 38x + 325 = 0. Solving this gives x = 25 or x = 13. If x = 13, x-18 is negative. So x = 25. The sides are 25, 24, 7. Perimeter = 25 + 24 + 7 = 56 units.

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