Discussion

If the perimeter of a right-angled isosceles triangle is (4√2+4) cm, then length of hypotenuse is?

Answer: A

The hypotenuse is 4 cm.

A right-angled isosceles triangle with equal sides \(a\) has hypotenuse \(a\sqrt{2}\), so

\[ \begin{aligned} 2a + a\sqrt{2} &= 4 + 4\sqrt{2} \\ a\sqrt{2}(\sqrt{2} + 1) &= 4(1 + \sqrt{2}) \\ a\sqrt{2} &= 4 \end{aligned} \]

Since \(a\sqrt{2}\) is the hypotenuse, it is 4 cm, and each leg is \(2\sqrt{2}\) cm. Check: \(2\sqrt{2} + 2\sqrt{2} + 4 = 4\sqrt{2} + 4\).

\(2\sqrt{2}\) cm is the length of each equal side, not the hypotenuse. 5 cm and 6 cm do not satisfy the perimeter.

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