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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Step 1: Let the other two sides be $x$ cm and $y$ cm. $x + y + 25 = 60 \Rightarrow x + y = 35$
Step 2: $y = 35 - x$
Step 3: By Pythagoras theorem: $x^2 + y^2 = 25^2 = 625$. Substituting: $x^2 + (35 - x)^2 = 625 \Rightarrow 2x^2 - 70x + 1225 = 625 \Rightarrow x^2 - 35x + 300 = 0$
Step 4: $(x - 20)(x - 15) = 0 \Rightarrow x = 20$ or $x = 15$
Step 5: If $x = 15$ then $y = 20$; if $x = 20$ then $y = 15$. Hence sides are $15$ cm and $20$ cm.

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