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The perimeter of a right triangle is $60$ cm and its hypotenuse is $25$ cm. Find the lengths of other two sides of the triangle.
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Let sides be $x, y$. $x + y + 25 = 60 \implies y = 35 - x$. $x^2 + y^2 = 25^2 \implies x^2 + (35 - x)^2 = 625 \implies x^2 - 35x + 300 = 0 \implies (x - 20)(x - 15) = 0 \implies x = 20, 15$. Sides are $15$ cm and $20$ cm.