Question

If the hypotenuse of a right-angled triangle is 13 and it's inradius is 5, then it's area = _____.

• A. 80 $c{m}^2$
• B. 70 $c{m}^2$
• C. 90 $c{m}^2$
• D. 100 $c{m}^2$

Answer 1

The correct option is C

90 $c{m}^2$

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$\frac{h+2r+h}{2}$

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

$\Rightarrow$ A = 5(13 + 5) = 5(18) = 90 $c{m}^2$