An architect is planning to make two triangular prisms out of iron.

The architect will use ∆ABC for the bases of one prism and ∆DEF for the bases of the other prism.

What is the scale factor from ∆ABC to ∆DEF?

Suppose the height of the prism made by ∆ABC is 15 inches. What is the volume of the prism made by ∆ABC?

Suppose the volume of the prism made by ∆ABC is 4459 〖"in" 〗^3.

What is the volume of the prism made by ∆DEF?

Part A:

In triangle ABC and DEF,

If the ratios of lengths of the sides of two triangles are same, then the triangles are similar.

Therefore ΔABC ΔDEF.

Scale factor of two triangles  =

Part B:

Suppose height of the prism made by ΔABC = 15 inches

Volume of the prism made by ΔABC = Area of the triangle × height

                                                             = 4410 inch³

Volume of the prism made by ΔABC = 4410 inch³

Part C: Suppose the volume of the prism made by ΔABC = 4459 inch³

Volume of the larger prism = (Scale factor)² × volume of the smaller triangle

Volume of the larger prism =   × volume of the smaller triangle

× volume of the smaller triangle

volume of the smaller triangle

Volume of the smaller triangle ΔDEF = 2275 inch³

3201

step-by-step explanation: