SOLUTION: 1. The sides of the quadrilateral are consecutive numbers. If the perimeter is 162, how long is each side?

Algebra ->  Equations -> SOLUTION: 1. The sides of the quadrilateral are consecutive numbers. If the perimeter is 162, how long is each side?      Log On


   

Question 252629: 1. The sides of the quadrilateral are consecutive numbers. If the perimeter is 162, how long is each side?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = length of first side.

Since "The sides of the quadrilateral are consecutive numbers", this means that the side lengths are: x, x+1, x+2, and x+3. Also, because the perimeter is 162, we know that x%2Bx%2B1%2Bx%2B2%2Bx%2B3=162 (just add up the four sides and set the sum equal to 162).

x%2Bx%2B1%2Bx%2B2%2Bx%2B3=162 Start with the given equation.


4x%2B6=162 Combine like terms on the left side.


4x=162-6 Subtract 6 from both sides.


4x=156 Combine like terms on the right side.


x=%28156%29%2F%284%29 Divide both sides by 4 to isolate x.


x=39 Reduce.


----------------------------------------------------------------------

Answer:

So the solution is x=39 giving the four sides to be:

x = 39
x+1 = 40
x+2 = 41
x+3 = 42