Question 44
A right-angled triangle has inradius 12 cm and circumradius of 25 cm. What is the area (in cm2) of the triangle?
Solution
In a right angled triangle
circumradius = Hypotenuese/2.
==> H = 2*25 = 50 cm.
inradius = $$\frac{a+b-H}{2}$$.
==> a + b = 74 cm.
Inradius is also equal to $$\frac{Area}{S}$$.
S = half of a + b + H = half of (50+74) = 62 cm.
Area = inradius * S = 12 * 62 = 744 sq. cm.
