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Question
In the below fig. ∠AOB = 90°, AC = BC, OA = 12 cm and OC = 6.5 cm. Find the area of
ΔAOB.
Solution
Since, the midpoint of the hypotenuse of a right triangle is equidistant from the vertices
∴ CA = CB = OC
⇒ AB = 13 = 6.5cm
In a right angle triangle OAB, we have
AB2 = OB2 + OA2
⇒ 132 = OB2 + 122
⇒ OB2 = 132 - 122 = 169 - 144 = 25
⇒ OB = 5
∵ ar (ΔAOB) = `1/2` (OA×OB) = `1/2` (12 ×5 ) = 30cm2
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