#### Answer

The lengths of the sides are 8, 12, 20, and 28.

#### Work Step by Step

The ratio of the sides is 2:3:5:7. The total perimeter is 68.
The sides therefore must be equal to 2, 3, 5, and 7 multiplied by the same number and then added to a total of 68. We'll call this number x.
First we have to solve for x
2x + 3x + 5x + 7x = 68
Simplify
17x = 68
Divide each side by 17
x = 68 $\div$ 17
x = 4
Now we return to the sides 2x, 3x, 5x, and 7x.
2(4) = 8
3(4) = 12
5(4) = 20
7(4) = 28