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Question

If the hypotenuse of a right-angled triangle is h and it's inradius is r, then it's area = _____.


A

h + r

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B

rh

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C

r(h + r)

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D

r2h

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Solution

The correct option is C

r(h + r)


Let PB = BQ = r

AP = AR = b - r

CQ = CR = a - r

AR + CR = h

a + b - 2r = h

a + b = h + 2r

Area = A = rS

A = ra+b+h2

A = rh+2r+h2

A = r(h + r)


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