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If the perimeter of the figure at right is x+38, what are the lengths of the sides and the value of the perimeter? 

 May 22, 2017
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Perimeter is the total length of all sides, so to get the perimeter of this figure, add up all the sides and set it equal to x+38:

 

\(x+x+3+x-5+x-4+x-1+x-1+x-2=x+38\)

 

Combine the like terms on the left side of the equation:

 

\(7x-10=x+38\)   Add 10 to both sides

\(7x=x+48\)   Subtract x from both sides

\(6x=48\)   Divide by 6 on both sides

\(x=8\)

 

Now that we have solved for x, let's plug it into the side lengths to get each of its values:

Side length 1\(=x=8units\)

Side length 2\(=x+3=8+3=11units\)

Side length 3\(=x-5=8-5=3units\)

Side length 4\(=x-4=8-4=4units\)

Side length 5\(=x-1=8-1=7units\)

Side length 6\(=x-1=8-1=7units\)

Side length 7\(=x-2=8-2=6units\)

 

Last thing we have to find is the perimeter. Simply evaluated x+38 and you are done:

 

\(P=x+38=8+38=46units\)

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 May 22, 2017

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