Consider obtuse angled triangles with sides 8 cm, 15
cm and x cm. If x is an integer, then how many such triangles exist?

(1)5 (2)21 (3)10 (4) 15 (5) 14

Solution follows here:

Solution:

(1)5 (2)21 (3)10 (4) 15 (5) 14

Solution follows here:

Solution:

Here two theorems come into picture.

One is Pythagoras for obtuse triangle: c

^{2}>a^{2}+b^{2}, where c is the biggest side of the three
Second one is Triangle inequality theorem: Sum of two
sides of a triangle must be greater than the measure of the third side. c < a+b, where c is the biggest side of
the three.

__Case-I: x is the biggest side:__

All possibilities of x according to triangle
inequality theorem, are 22,21,20,19,18,17,16,15.

But 8

^{2}+15^{2}= 64+225 = 289 = 17^{2}, hence as per Pythagoras, we can consider values above 17 only. x=22,21,20,19,18__Case-II: 15 is the biggest side:__

All possibilities of x according to triangle
inequality theorem, are 8,9,10,11,12,13,14.

But 15

^{2}- 8^{2}= 225-64 = 161 < 13^{2}, hence as per Pythagoras, we can consider values less than 13 only. x=8,9,10,11,12
All possible values of x = 8,9,10,11,12,18,19,20,21,22

Total 10 values

Answer(3)
good one

ReplyDeleteIs 15 given ist step possible as x must be greater than 15

ReplyDeleteCan x take as given in 1st step. as x must be greater than 15

ReplyDelete