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

1 Answer
Dec 8, 2016

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.