We know that the perimeter of triangle is sum of three sides   .... step(1)

So P=Lengths of A+B+C =35

but we know A is Length of B times2 , techniqually A=2B and C=A+5

Plug the' A 'and C values in the above equation A+B+C=35  we get 2B+B+A+5=35

3B+2B+5=35 

5B=30

B=6

plug the value for B in A=2B we get A=12

and C=A+5 which is 12+5=17

We have 3 Equations:

Eq.1) 35=A+B+C

Eq. 2) A=2B

Eq. 3) C=A+5

Notice that all three equations have the variable A.  What we want to do is to replace B and C in Eq. 1 in terms of A.  If we solve Eq. 2 for B, we get that B=(1/2)A.  Note that in Eq. 3, C is already solved in terms of A.  Now we substitute B=(1/2)A and C=A+5 in to Eq. 1:

35=A+(1/2)A+A+5 (Add like terms)

35=2.5A+5 (subtract 5 from both sides)

30=2.5A (divide by 2.5 on both sides)

A=12

Now plug in A=12 in to Eq. 2, and we find that B=6.

Finally, plug A=12 in to Eq. 3, and we find that C=17.

So P=A+B+C, and 35=12+6+17

Additionally, you can also put Eq. 1 in terms of B as the other answer states, and solve for B.

I hope that helps!

Here's a hint. Put C in terms of B. Then you will have A, B, and C in terms of B. Then work with the original equation.