Example

Two similar right square prism sculptures are in the same park, as shown below.

Find the edge length of the height of the larger square prism.

Step 1: Identify the right triangle in the smaller prism by clicking on a part that represents a side of the right triangle.

Step 2: Identify a second right triangle with a similar orientation in the larger prism by clicking on a part of the figure that represents a side of the right triangle.

Step 3: Determine whether or not the smaller triangle has side lengths that are a Pythagorean triple. If so, then identify the Pythagorean triple. Interactive button. Assistance may be required. ____________________ Yes, the length of the longer leg is the height of the prism, or 12 feet and the length of the hypotenuse is the length of the diagonal of the front face of the prism, or 13 feet, the Pythagorean trip is 5, 12, 13 - since the length of the longer leg of the right triangle is 12 feet and the length of the hypotenuse is 13 feet.

Step 4: Since the prisms are similar, use the known length of the larger prism to identify the scale factor that can be multiplied by the dimensions of the smaller prism to generate the larger prism. The scale factor is Interactive button. Assistance may be required. ____________________ 3 -To determine the scale factor, divide the length of the edge of the larger prism by the length of the corresponding edge of the similar prism.

Step 5: Apply the scale factor to all the sides of the right triangles:

• 12 ⇒ Interactive button. Assistance may be required. ____________________ 36
• 13 ⇒ Interactive button. Assistance may be required. ____________________ 39
• 5 ⇒ Interactive button. Assistance may be required. ____________________ 15

Step 6: The edge length of the base of the larger square prism is Interactive button. Assistance may be required. ____________________ 15 feet

There are six figures below. Match the figures so that the two similar figures are in a column together.