Chapter 8, Problem 8SAP

To determine

To find: correct option that gives the required number of red tiles.

Explanation of Solution

Given information:

Let the length and breadth of rectangular surface be $l\text{ and }b$ .

  $\begin{array}{l}l=30\text{ inch}\\ b=40\text{ inch}\end{array}$

Let the area of each white tiles and area of each red tiles be $A_w\text{ and }{A}_r$ respectively. White tiles cover the interior surface and red tiles covers the edge of the rectangular surface only.

  $A_w=A_r=1\text{ inche square}$

The options are as follows:

1. 70
2. 136
3. 140
4. 142
5. 144

Calculation:

First draw a figure for the given situation as follows:

The length and breadth of interior rectangle can be evaluated as follows:

  $\begin{array}{c}{l}_w=l-2l_r\\ =30-2\left(1\right)\\ =28\\ b_w=b-2b_r\\ =40-2\left(1\right)\\ =38\end{array}$

The number of red tiles $\left(\text{let }n\right)$ can be evaluated as follows:

  $\begin{array}{c}n{A}_r=\text{Area of total rectangular surface }-\text{Area of interior rectangular surface}\\ n\left(1\right)=\left(lb\right)-\left(l_w{b}_w\right)\\ =\left(30\times 40\right)-\left(28\times 38\right)\\ =1200-1064\\ =136\end{array}$

Since the number of red tiles required is 136. So, option B. is correct.