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

Option C:

The scale factor of the larger prism to the smaller prism is $\frac{21}{19}$.

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

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

                           $=\frac{\sqrt {441} }{\sqrt{361}}$

                           $=\frac{\sqrt {21^2} }{\sqrt{19^2}}$

Both square and square roots are cancelled, we get

                            $=\frac{21}{19}$

The scale factor of the larger prism to the smaller prism is $\frac{21}{19}$.

Hence Option C is the correct answer.