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

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:

 

$P=x+38=8+38=46units$