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Question
In ΔABC, AB = 9 cm, BC = 40 cm, AC = 41 cm. State whether ΔABC is a right-angled triangle or not. Write reason.
Sum
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Solution
Sides of ΔABC are AB = 9 cm, BC = 40 cm, AC = 41 cm
The triangle's longest side measures 41 cm.
∴ (41)2 = 1681 ......(i)
Now, the total of the remaining sides squared is
(9)2 + (40)2 = 81 + 1600
= 1681 ......(ii)
From equations (i) and (ii), the given sides form a right-angle triangle.
Because the square of the longest side equals the sum of the squares of the remaining two sides. .....[Converse of Pythagoras theorem]
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