## A triangular sail has a perimeter of 25 m. Side a is 2 m shorter than twice side b, and side c is 3 m longer than side b. How do you find the length of each side?

A is 10, B is 6, and C is 9.

Our solution centers around the length of side B, as once you have that value, you can solve for A and B very easily. Let’s develop equations for what we can, first.

A = (2B-2) B = (Value Unknown) C = B+3

We know that a perimeter is the sum of all three sides. We can develop an equation for this. ##P = A+B+C##

Now, let’s sub in our equations we made earlier. ##25 = (2B-2)+(B)+(B+3)##

Now we simplify to isolate B, thus retrieving the value of this variable.

##25 = 2B + 2B + 1##

##25-1 = 4B##

##24 = 4B##

##24/4 = 4B/4##

##B= 6##

From here, we can just follow through with the instructions from the question to find A and C, or sub in B to our equations that we made earlier.

##A = (2B-2)##

##A = (2*6(-2))##

##A = 10##

##C = B+3##

##C = 6+3##

##C= 9##

To double check that we have the correct answer, we sub these back into our perimeter equation and ensure that both sides equal each other.

##25 = A+B+C##

##25 = 10+6+9##

##25 = 25##

It lines up, so we have gotten the correct answers. A is 10, B is 6, and C is 9.

Cheers, k