Chapter 12, Problem 16CR

To determine

To find: The ratio perimeter of small and big pyramid.

Answer to Problem 16CR

The ratio of perimeters of $\Delta \text{RST}$ and $\Delta \text{XYZ}$ is $1:3$ .

Explanation of Solution

Given information: Plane RST and XYZ are parallel. Also, $VS:VY=1:3$ .

  

Calculation:

The ratio of the corresponding sides of any two similar geometric figures is termed as Scale factor. The theorem of similar solids states that if the scale factor of two similar solids is $a:b$ , then the ratio of perimeters is $a:b$ .

It is given that $PlaneRST\parallel PlaneXYZ$ and $\Delta RST\sim \Delta XYZ$ . The scale factor of two triangles will be 1:3.

Now, the ratio of the perimeters of both triangles is:

  $\frac{\text{Perimeter of }\Delta RST}{\text{Perimeter of }\Delta \text{XYZ}}=\frac{1}{3}$

Therefore, ratio of total area pyramid is $1:3$ .