Question

how many triangles can be formed having perimeter 45?

Answer 1

An infinite number.

How many real numbers are there between 0 and 45? Start with 0, then 0.1, or 0.01, 0.001, and so on. There's a limitless amount of possible side lengths.

Eg 20, 20, 5. Or 21, 19, 5. Or 15, 15, 15. Or 16.5, 13.5, 15. Or 10, 18, 17.

If the side lengths are a, b, c, then as long as two of those when added together are greater than the third side (ie a+b > c or c+a >b etc), and a+b+c = 45, you have a triangle.

Answer 2

is there any shortcut??

Answer 3

A shortcut to what...? listing every possibility, when there's unlimited possibilities?

Answer 4

how many triangles can be formed having perimeter 45?
shortcut to this..
let suppose we have perimeter as 666..then answer is.???

Answer 5

Er, what? If the perimeter is 45, then the perimeter can not also be 666.

Answer 6

i mean if ques comes up with permeter as 666 instead of 45
?

Answer 7

Then there's limitless possibilities. Even more limitless than before, if you will, since there's "more" possible real numbers.

Answer 8

so no solution???

Answer 9

No. Limitless means infinite solutions.

Answer 10

but i have ques having four options...what to do in that case/???

Answer 11

What are the four options? And it's possible you haven't posted the question correctly... as it doesn't seem like a typical question.

Answer 12

in the question we have the information a+b+c =45; also a,b,c >0
and we know a+b >c ; b+c > a; a+c > b
so if we put a+b = 45-c in the first inequality we will get 45-c >c which gives 22.5 >c
similarly we will have a < 22.5 and b < 22.5
so now there can be infinite different values of a,b,c which will satisfy this condition

Answer 13

a, b, and c are integer numbers or not ?

Answer 14

there is no information in the question about a,b,c being integer

Answer 15

a,b,c are integers

Answer 16

Ohh then it gets interesting
we have three numbers 0<a,b,c <22.5
A B C
22 22 1
22 21 2
.
..keep reducing B and adding to C
..
22 12 11

so we will get 11 ways and we can interchange the values of A B C in 3! way
so answer will be 3!*11 =66

Answer 17

ankit..r u sure with the ans???

Answer 18

No sry made a mistake we will have 10*3!+3!/2=60+3 triangles
63 is there an option for 63?

Answer 19

nopes..

Answer 20

a. 53
b.50
c.48
d.45

Answer 21

@puesh not sure where is the error...did you understood what I was doing? You can check for any silly mistakes

Answer 22

not able to find any mistake in this, but answer is not correct.