Question

A triangle has two sides that measure 2.5 cm and 16.5 cm. Which could be the measure of the third side?

Answer 1

Third side will have a value between `14` and `19`.

Explanation:

As the two sides measure `2.5` `cm.` and `16.5` `cm.`, let the included angle between them be `theta`.

It is evident that `0^o < theta < 180^o`.

Then using the cosine formula of solving triangles,

the square on the third side will be given by

`2.5^2+16.5^2-2xx2.5xx16.5xxcostheta`

`=6.25+272.25-82.5costheta`

`=278.5-82.5costheta`

and as `0^o < theta < 180^o`, `-1 < costheta < 1`

Hence the third side say `x` will be given by

`sqrt(278.5-82.5) < x < sqrt(278.5+82.5)`

or `sqrt196< x< sqrt361`

or `14 < x <19`.

Hence third side will have a value between `14` and `19`.