Question
What is the length of the hypotenuse in an isosceles right-angled triangle if one of its equal sides measures 6√2 cm?
Solution
ATQ, Since ΔABC is an isosceles right-angled triangle, then AC = AB ⇒ AC = AB = 6√2 cm (Given) Now, using the Pythagoras theorem, we get BC² = AC² + AB² ⇒ BC² = AB² + AB² ⇒ BC² = 2AB² ⇒ BC² = 2(6√2)² ⇒ BC² = 2(36 × 2) ⇒ BC² = 144 ⇒ BC = 12 cm Hence, the length of the hypotenuse is 12 cm.
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