Question

A sculptor is planning to make two triangular prisms out of steel. The sculptor will use △ABC for the bases of one prism and △DEF for the bases of the other prism.

(a)Is △ABC similar to △DEF? Explain.
(b)Suppose the sculptor makes both prisms with the same height. Which prism will have a greater volume? How many times greater? SHOW YOUR WORK FOR BRAINLIEST!!

Answer 1

Answer:

a)

Verify is the corresponding sides have same ratio:

• AB / DE = 50/60 = 5/6
• BC / EF = 20/24 = 5/6

Since the ratios are same, the triangles are similar

b)

If one dimension is same, the base areas will make difference by the square of the scale factor:

• (6/5)² = 1.44 times