Question

find area of a triangle whose altitude are 10cm, 12cm and 15cm​

Answer 1

Step-by-step explanation:

Hi!

Here you go:-

Ratio of altitudes : 10:12:15.

Since Area of Triangle = (1/2) x Base x Height -(1)

For a given area the height and the base are inversely proportional.

Thus, ratio of bases => (1/10): (1/12):(1/15)

Multiplying throughout by the LCM = 60,

The ratio of sides => 6:5:4.

OR the sides would be 6a, 5a and 4a cms respectively and their corresponding altitude will be 10,12 and 15 cms respectively.

Now, from 1, Area of triangle = (1/2) x 6a x 10

Also, Area = Inradius x Semiperimter = (r) x (6a+5a+4a)/2.

Equating the two,

30a = (15a/2) x r

OR r = 4 cm.

Hence, area of incircle = pi x (r^2) = 3.14 x (4^2) = 3.14 x 16 = 50.24 cm^2.