Find the lengths of the three sides.

Question

The length of Side b of a triangle is 6 m less than twice the length of Side A. Sides B and C have the same length. If the perimeter is 28 m, then what are the lengths of the three sides.

Answer 1

First, translate the information they give you from words into equations. This is what we know...

1) a + b + c = 28

2) b = c

3) b = 2a - 6

 

Because we have three variables and three equations, we know we can solve this problem. The next goal is to have one equation with one variable, let's say "b" since this is the variable found in all three equations. So we need to replace the "a" and "c" in the first equation with an expression in terms of "b."  b = c is quite straightforward. Then for the equation b = 2a - 6, if you solve for "a" for an expression in terms of "b," you get a = (b + 6)/2.

 

Now, you plug the information we just figured out into the first equation, which will look like this...

[(b + 6)/2] + b + b = 28

 

Then, simply solve for "b." Use this answer to solve for "a" and "c" from equations two and three. 

 

The answer should be a=8m, b=10m, and c=10m.

Answer 2

Here's what we know:

a + b + c = p

b = 2a - 6

c = b

p = 28

 

Since we have values, we can put them into our equation:

a + 2a - 6 + 2a - 6 = 28

Now we combine like terms:

5a - 12 = 28

Time to isolate a. Add 12 to both sides:

5a = 40

divide by 5:

a = 8

 

Now that we have a, we can solve for b and c:

2 * 8 - 6 = b & c

16 - 6 = 10 = b & c

 

Now to check our answer:

8 + 10 + 10 = 28

28 = 28

So the three sides are: 8m, 10m, and 10m.