Question

The area of the triangle shown is represented by A=s(s−21)(s−17)(s−10)−−−−−−−−−−−−−−−−−−−−√, where s is equal to half the perimeter. What is the height h of the triangle?

Answer 1

9.88 units

Explanation:

We are given that area of triangle is given by

`A=√(s(s-21)(s-17)(s-10))`

s=Half perimeter

By comparing with

`A=√(s(s-a)(s-b)(s-c))`

We get

a=21

b=17

c=10

`s=(a+b+c)/(2)=(21+17+10)/(2)=24`

Now, the area

`A=√(24(24-21)(24-17)(24-10))`

A=84

Area of triangle,
`A=(1)/(2)* bh`

b=17

`84=(1)/(2)(17)(h)`

`h=(84* 2)/(17)`

`h=9.88 units`

Hence, the height of the triangle=9.88 units