Chapter 13.2, Problem 28SR

To determine

To calculate: The missing measure in the given similar pair of solids.

Answer to Problem 28SR

The missing measures are x = 50 cm and y = 36 cm.

Explanation of Solution

Given information:A pair of similar figures given. Length, width and height of one cuboid are x cm, 24 cm and 30 cm. Length, width and height of other cuboid are 75 cm, y cm and 45 cm.

Calculation:

Two similar cuboidsare given.

Thus it can be written that,

  $\begin{array}{l}\frac{x}{75}=\frac{30}{45}\\ \Rightarrow x\times 45=30\times 75\\ \Rightarrow 45x=2250\\ \Rightarrow x=\frac{2250}{45}\\ \Rightarrow x=50\end{array}$

  $\therefore$ The missing side x = 50 cm.

Also we will get,

  $\begin{array}{l}\frac{24}{y}=\frac{30}{45}\\ \Rightarrow y\times 30=24\times 45\\ \Rightarrow 30y=1080\\ \Rightarrow x=\frac{1080}{30}\\ \Rightarrow y=36\end{array}$

  $\therefore$ The missing side y = 36 cm.