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प्रश्न
In a right-angled triangle, the lengths of sides containing the right angle are 20 cm and 21 cm. What is the radius of the circumcircle of the triangle?
बेरीज
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उत्तर
There is a right-angled triangle.
In question it is given that the lengths of sides containing the right angle are 20 cm and 21 cm.
Suppose Perpendicular = 20 cm
Base = 21 cm
Hypotenuse = ?
Then, (Hypotenuse)2 = (Perpendicular)2 + (Base)2
(Hypotenuse)2 = (20)2 + (21)2
(Hypotenuse)2 = 400 + 441
(Hypotenuse)2 = 841
Hypotenuse = `sqrt(841)`
Hypotenuse = 29 cm
According to the theorem the radius of a circumcircle of a right-angled triangle is equals to the half of the hypotenuse of the triangle.
Hence, the radius = `29/2` cm = 14.5 cm.
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