A triangle has sides with lengths 13 cm, 14 cm and
15 cm. A circle whose centre lies on the longest side
touches the other two sides. The radius of the circle
is (in cm)
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Radius of circle = 56/9 cm
Step-by-step explanation:
Triangle has three sides
13 , 14 , 15
s = (13 + 14 + 15)/2 = 21
Area of triangle PQR= √21(21-13)(21-14)(21-15)
= √21 * 8 * 7 * 6
= √7 * 3 * 2 * 2 * 2 * 7 * 2 * 3
= 7 * 3 * 2 * 2
= 84
join PO
Area of PQR = Area of POQ + Area of POR
R = radius of Circle
Area of Triangle = (1/2) PQ * R + (1/2)PR * R
= (1/2) 13R + (1/2) 14R
= 27R/2
27R/2 = 84
=> R = 168/27
=> R = 56/9
Radius of circle = 56/9 cm
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