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Chapter 8: Q. 48 (page 542)

If h1 , h2 , and h3 are the altitudes dropped from P, Q, and R, respectively, in a triangle (see the figure shown to the right), show that1h1+1h2+1h3=sK

Where K is the area of triangle ands=12(a+b+c)

Short Answer

Expert verified

We proved1h1+1h2+1h3=sK

Step by step solution

01

Given information

We are given,

02

Find the area of triangle

The area of triangle can be given as

K=ah12

Similarly it can also be given as

K=bh22AndK=ch32

03

Now Write the areas in terms of a,b,c

We get,

a=2Kh1b=2Kh2c=2Kh3

04

Now substitute the values in the formula of s

We have

s=12(a+b+c)s=12(2Kh1+2Kh2+2Kh3)s=Kh1+Kh2+Kh31h1+1h2+1h3=sK

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