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The hypotenuse of a right-angled triangle is 25 cm and its perimeter 56 cm. Find the length of the smallest side.

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The hypotenuse of a right-angled triangle is 25 cm and its perimeter 56 cm. Find the length of the smallest side.

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AB + BC + CA = 56 cm

AC = 25 cm

AB + BC = 56 – 25 = 31

AB2 + BC2 = AC2

(AB + BC)2 – 2AB . BC = AC2 [∵ a2 + b2 = (a + b)2 – 2ab]

312 – 2AB . BC = 252

-2AB . BC = 625 – 961

∴ The length of the smallest side is 7 cm.

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