Question
Find the hypotenuse of an isosceles right-angled
triangle where each of the equal sides is 7√5 cm.Solution
AATQ, Since ΔABC is an isosceles right-angled triangle, then AC = AB ⇒ AC = AB = 7√5 cm (Given) Now, using the Pythagoras theorem, we get BC² = AC² + AB² ⇒ BC² = AB² + AB² ⇒ BC² = 2AB² ⇒ BC² = 2(7√5)² ⇒ BC² = 2(49 × 5) ⇒ BC² = 490 ⇒ BC = √490 = 7√10 cm Hence, the length of the hypotenuse is 7√10 cm.
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