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Standard IX

Mathematics

Pythagoras Theorem

If ABC is a r...

Question

If $△$ ABC is a right angled triangle with $∠$ B = 90°, AB = 15 units and BC = 112 units, find its third side ___.

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Solution

By Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Since in this triangle, the third side is the side opposite to the right angle and hence is the hypotenuse, we must have,
$\Rightarrow$ $A C^{2} = 15^{2} + 112^{2}$
$\Rightarrow A C = \sqrt{12769} = 113$ units

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If △ABC is a right angled triangle with ∠B = 90°, AB = 15 units and BC = 112 units, find its third side ___.

By Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Since in this triangle, the third side is the side opposite to the right angle and hence is the hypotenuse, we must have, ​⇒ AC2=152+1122 ⇒AC=√12769=113 units

If $△$ ABC is a right angled triangle with $∠$ B = 90°, AB = 15 units and BC = 112 units, find its third side ___.