The two triangular prisms shown are similar. The dimensions of the larger prism were multiplied by a scale factor of to create the smaller prism. When the large prism was reduced, the surface area changed by a factor of . . . .

16/25 (B)

The complete question related to thus found on (ID: 10153234) is stated below:

The two triangular prisms shown are similar. The dimensions of the larger prism were multiplied by a scale factor of to create the smaller prism.

When the large prism was reduced, the surface area changed by a factor of

A. 64/125

B. 16/25

C. 4/5

D. 10/8

Find attached the diagram

Step-by-step explanation:

In dilation, two figures have same shape but different size.

The triangular prism was dilated to create a new prism.

The larger triangular prism is the original shape

The smaller triangular prism is the new shape

Let the scale factor = p

For larger prism: the length = breadth = height = 10unit

For smaller prism: the length = breadth = height = 8unit

Surface area of smaller triangular prism = p × surface area of larger triangular prism

p = (Surface area of smaller triangular prism)/(surface area of larger triangular prism)

In similar shapes, the ratio of their areas = square of the ratio of their corresponding sides.

Let's take the height of each shape

Ratio of their corresponding sides (height) = 8/10

p = ratio of areas = (8/10)²

p = 64/100

p = 16/25