Question

In a triangle ABC,if [1/(a+c)]+[1/(b+c)]=3/(a+b+c) then c is equal to??

Answer 1

a,b, c are angles

Answer 2

?can u help ash

Answer 3

@satellite73 , @AccessDenied , @campbell,

Answer 4

A, B, C are the angles and a, b, c are the sides? this is standard....

Answer 5

ys i made a a mistake of using small letters thats why i told they are angles

Answer 6

i guess a start is
\[\frac{1}{a+c}+\frac{1}{b+c}=\frac{1}{120}\]

Answer 7

180 !!

Answer 8

oops right

Answer 9

\[\frac{1}{a+c}+\frac{1}{b+c}=\frac{1}{60}\]

Answer 10

we can easily get rid of one of the variables, but i don't know how to get rid of two of them

Answer 11

Does c have to be a specific number? Or can it be given in terms of a and b?

Answer 12

my options are
a)30
b)60
c)75
d)90

Answer 13

By method of mostly guess and check, answer b is correct.

A 60-60-60 triangle satisfies the relationship.

Answer 14

any other logical explanation?

Answer 15

- so i think the first step will be 1/(a+c) +1/(b+c) = 3/(a+b+c) = 3/180 = 1/60
- so than 1/(a+c) +1/(b+c) = 1/60
- if a+b+c=180 so than a=180-b-c

- than 1/(180-b-c+c) +1/(b+c) = 1/60

1/(180-b) +1/(b+c) =1/60

- how you think please this is one right way or ... ?

Answer 16

You can simplify your original equation to\[c = {(-a b+60 a-b^2+120 b)\over(a+b-60)}\]From there, I used wolfram alpha to let \(c=30, 60, 75, 90\) until I got a solution in integers that fit the relationship.

Answer 17

THANKS A LOT SEE IF U CAN HELP HERE
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Answer 18

For that matter however, a=40, b=65, c=75 also works.

Answer 19

So answer c. could also be correct :/