#### Answer

24 cm, 28 cm, 36 cm

#### Work Step by Step

Set the smallest side length equal to x.
Then according to the extended ratio 6:7:9, the middle side length is equal to $\frac{7}{6}$x, and the largest side length is equal to $\frac{9}{6}$x.
Given the perimeter is equal to 88, we set up the following equation: x + $\frac{7}{6}$x + $\frac{9}{6}$x = 88
$\frac{22}{6}$x = 88
x=24
To solve for the other two sides, we have:
$\frac{7}{6}$x = $\frac{7}{6}$(24) = 28 and $\frac{9}{6}$x = $\frac{9}{6}$(24) = 36