Question

The surface areas of two similar rectangular prisms are 361 m2 and 441 m2. What is the scale factor of the larger prism to the smaller prism?

Answer 1

C.

Explanation:

Answer 2

Option C:

The scale factor of the larger prism to the smaller prism is
`(21)/(19)`.

Solution:

Two rectangular prisms are similar.

Surface area of the smaller prism = 361 cm²

Surface area of the larger prism = 441 cm²

Scale factor of larger prism to smaller prism

`$=\frac{\sqrt \text{{Surface area of larger prism}} }{\sqrt\text{{Surface area of smaller prism} }}`

`$=\frac{\sqrt {441} }{√(361)}`

`$=\frac{\sqrt {21^2} }{√(19^2)}`

Both square and square roots are cancelled, we get

`$=(21)/(19)`

The scale factor of the larger prism to the smaller prism is
`(21)/(19)`.

Hence Option C is the correct answer.