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If the length of hypotenuse of a right angled triangle is 5 cm and its area is 6 sq cm, then what are the lengths of the remaining sides?

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Let one of the remaining sides be x cm.

Then, other side = \(\sqrt{5^2-x^2}\) cm

∴ Area = \(\frac{1}{2}\times{x} \times\sqrt{25-x^2}\) = 6

⇒ \(x\sqrt{25-x^2}\) = 12 ⇒ x2(25 – x2) = 144

⇒ 25x2 – x4 = 144 ⇒ x4 – 25x2 + 144 = 0 

⇒ (x2 – 16) (x2 – 9) = 0 

⇒ x2 = 16 or x2 = 9 ⇒ x = 4 or 3

The two sides are 4 cm and 3 cm.

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