# The perimeter of a triangle is 18 feet. The second side is two feet longer than the first. The third side is two feet longer then the second. What are the lengths of the sides?

Feb 10, 2016

Let the first side of the triangle be called A, the second side B and the third side C. Now, use the information from the problem to set up the equations ...

#### Explanation:

$A + B + C = 18$
$B = A + 2$
$C = B + 2 = \left(A + 2\right) + 2 = A + 4$ [ substitution from 2nd equation]

Now, rewrite equation 1:

$A + B + C = A + \left(A + 2\right) + \left(A + 4\right) = 18$

Simplify ...

$3 A + 6 = 18$
$3 A = 12$
$A = 4$

So, side A = 4. Now use this to solve for sides B and C ...

$B = A + 2 = 4 + 2 = 6$

$C = A + 4 = 4 + 4 = 8$

So, $\Delta A B C$ has sides $4 , 6 , \mathmr{and} 8$, respectively.

Hope that helped!

Feb 10, 2016

Assuming the shortest side measures x, the second side would measure x + 2 and the third x +4, since the 3rd is 2 longer than the second.

#### Explanation:

x + x + 2 + x + 4 = 18

3x + 6 = 18

3x = 12

x = 4

The sides measure 4, 6 and 8 feet.