Question 122569
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Discussion
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<p style="font: courier">
The perimeter of a general trapezoid is simply the sum of the 4 sides.

{{{P[T]=s[1]+s[2]+s[3]+s[4]}}}

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Solution
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You are given expressions for the 4 sides:
{{{s[1]=x+27}}}
{{{s[2]=x+74}}}
{{{s[3]=x+274}}}
{{{s[4]=x}}}

And you are given the perimeter, {{{P[T]=3279}}}


Although the problem doesn't state, you must assume that the constant values
in the expressions for three of the sides are in feet since the perimeter is
given in feet.  Without this assumption, the problem cannot be solved as
stated.

Combining the given information into the formula for the perimeter we have:
{{{(x+27)+(x+74)+(x+274)+x=3279}}}


Combining like terms we have:
{{{4x + 375=3279}}}


Add -375 to both sides:
{{{4x=2904}}}


And divide by 4:
{{{x=726}}}

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<h3 style="font: bold times">
Check Answer
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<p style="font: courier">
{{{s[1]=726+27=753}}}
{{{s[2]=726+74=800}}}
{{{s[3]=726+274=1000}}}
{{{s[4]=726}}}

and
{{{753+800+1000+726=3279}}}: Answer checks.
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