+647 If the perimeter of the figure at right is x+38, what are the lengths of the sides and the value of the perimeter? 
+2446 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:
\(P=x+38=8+38=46units\)
