A frustum of a right pyramid has a rectangular base ABCD with AB=12cm and BC=9cm. The top rectangular face EFGH has EH=8cm and the height of the frustum is 10cm. Find the length of GH.

Here's the solution to the frustum problem:

Given Information:

• Frustum of a right pyramid with rectangular base ABCD.
• $AB = 12$ cm, $BC = 9$ cm.
• Top rectangular face EFGH with $EH = 8$ cm.
• Height of the frustum ($h$) = 10 cm.

Part (a): Find the length of GH.

Step 1: Determine the ratio of similarity between the top and bottom bases.
Since the frustum is from a right pyramid with a rectangular base, the top face EFGH is similar to the bottom face ABCD.
The ratio of corresponding sides is constant. We can use the sides $EH$ and $BC$.
Ratio