Chapter 6, Problem 8CST

To determine

To calculate: the dimensions of the smallest rectangle.

Answer to Problem 8CST

the dimensions of the smallest rectangle are \ $7.68inches$ and $5.12inches$ .

Explanation of Solution

Given information :

Width of smallest rectangle = $\frac{4}{5}$ width of the medium sized rectangle

Width of medium sized rectangle = $\frac{4}{5}$ width of the largest rectangle

Largest rectangle length= $12inches$

Largest rectangle width = $8inches$

Calculation : to find the dimensions of the smallest rectangle,

Width of medium sized rectangle = $\frac{4}{5}$ width of the largest rectangle

Width of medium sized rectangle = $\frac{4}{5}·8$

Width of medium sized rectangle = $6.4inches$

Width of smallest rectangle = $\frac{4}{5}$ width of the medium sized rectangle

Width of smallest rectangle = $\frac{4}{5}·6.4inches$

Width of smallest rectangle = $5.12inches$

Because rectangles are similar so their length ratio will be same as their width,

Length of medium sized rectangle = $\frac{4}{5}$ length of the largest rectangle

Length of medium sized rectangle = $\frac{4}{5}·12$

length of medium sized rectangle = $9.6inches$

length of smallest rectangle = $\frac{4}{5}$ length of the medium sized rectangle

length of smallest rectangle = $\frac{4}{5}·9.6inches$

length of smallest rectangle = $7.68inches$

Hence, the probability of the choose slip number is greater than $5$ is $\frac{3}{8}$ .