Question
What is the length of the hypotenuse in an isosceles
right-angled triangle if one of its equal sides measures 5√3 cm?Solution
ATQ, 
ATQ, Since ΔABC is an isosceles right-angled triangle, then AC = AB ⇒ AC = AB = 5√3 cm (Given) Now, using the Pythagoras theorem, we get BC² = AC² + AB² ----(1) ⇒ BC² = AB² + AB² [Using (1)] ⇒ BC² = 2AB² ⇒ BC² = 2(5√3)² ⇒ BC² = 2(25 × 3) ⇒ BC² = 150 ⇒ BC = √150 = 5√6 cm Hence, the length of the hypotenuse is 5√6 cm.
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