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

h + r

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r(h + r)

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$r^{2}$ h

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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

$\Rightarrow$ A = r $\frac{a + b + h}{2}$

$\Rightarrow$ A = r $\frac{h + 2 r + h}{2}$

$\Rightarrow$ A = r(h + r)

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

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)

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

$\Rightarrow$ A = r $\frac{a + b + h}{2}$

$\Rightarrow$ A = r $\frac{h + 2 r + h}{2}$

$\Rightarrow$ A = r(h + r)