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#.