plse solve this

Question

plse solve this

wolf1728 · Answer

any more description to this?  What is A.P. ? Any graphics with this?

anonymous · Answer

no...

anonymous · Answer

one

anonymous · Answer

hw

anonymous · Answer

@Directrix

directrix · Answer

I worked on this when you first posted it and did not get anywhere. Sorry to be of no  help.

anonymous · Answer

k

wolf1728 · Answer

And what is A.P. ?

directrix · Answer

@wolf1728  I think it is Arithmetic Progression.

I was wondering about right triangles and Pythagorean triples such as 3,4,5 and then 

15, 20, 25 and 12, 16, 20 but that led nowhere.

directrix · Answer

Arithmetic Progression and Arithmetic Sequence are the same, I think.

anonymous · Answer

@experimentX

rsadhvika · Answer

two questions on ur question :-

1) are they right triangles ?
2) and you want to solve them in integers ?

experimentx · Answer

given the second post ,,, there are infinite such triangles with smallest side 20

experimentx · Answer

if by that you mean right angle triangle, then your approach is correct.

experimentx · Answer

you might look into 5, 12, 13

hartnn · Answer

let me try....
sum of 2 sides of triangle must be > 3rd
the 3 sides are 
20, 20+d, 20+2d  (d is positive only)
so, 
20 + 20 +d > 20 +2d 
20 > d

20 + 20+2d >20 +d
d>-20 obviously

20+2d+20+d >20
3d >-20 also obviously

so, d can be less than 20 only...
like if d = 1 , 
20,21,22 
d=2 
20, 24, 26
......
till d= 19
20, 39, 58
so there are 19 such triangles 

i have not assumed a right triangle

experimentx · Answer

woops!! i forgot they were in AP.

anonymous · Answer

but how 20 came

hartnn · Answer

"If the shortest side is 20"
so, 1st term = 20, and other 2 terms > 20
hence d id positive

anonymous · Answer

but in question, the shortest side = 10 cm

hartnn · Answer

your question
"The sides of a triangle are in A.P. If the shortest side is 20, the number of such triangles are"

hartnn · Answer

if its 10, then, just replace 20 by 10
there will be 9 triangles then

anonymous · Answer

oops.ssrry

hartnn · Answer

did you get what i have done ?

anonymous · Answer

yes, i m seeing

anonymous · Answer

okay , i got it , but why till d = 19 has taken

hartnn · Answer

20 + 20 +d > 20 +2d 
20 > d
so d must be less than 20, but positive
so, d= 1 to 19

anonymous · Answer

okay 
thanks u so much , i got it

hartnn · Answer

welcome ^_^