Question 252629
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+x+1+x+2+x+3=162}}} (just add up the four sides and set the sum equal to 162).


{{{x+x+1+x+2+x+3=162}}} Start with the given equation.



{{{4x+6=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=(156)/(4)}}} Divide both sides by {{{4}}} to isolate {{{x}}}.



{{{x=39}}} Reduce.



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Answer:


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


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