Chapter 1.1, Problem 46E

(a)

To determine

To find the area of one rectangular mat when area of Square mat is half the area of one of the rectangular mats.

  

Answer to Problem 46E

The area of one rectangular mat is $18f{t}^2$ .

Explanation of Solution

Given:

Area of Square mat is half the area of one of the rectangular mats.

  

Calculation:

Given:

Area of Square mat is half the area of one of the rectangular mats.

Total area $=$$81f{t}^2$

Total number of rectangular mats $=4$

Now, let area of the rectangular mat be $x$ .

Thus, Area of Square mat $=$$\frac{1}{2}x$

And Total area of rectangular mats $=4x$

Now, as per the given statement, we have equation as:

  $\frac{1}{2}x+4x=81$

Solving the above equation, we have:

  $\begin{array}{l}\frac{x+8x}{2}=81\\ \frac{9x}{2}=81\\ x=18\end{array}$

Thus, the area of one rectangular mat is $18f{t}^2$ .

Conclusion:

Hence, area of one rectangular mat is $18f{t}^2$ .

(b)

To determine

To find the dimensions of a rectangular mat when length of rectangular mat is twice the width.

  

Answer to Problem 46E

The width is $3$ $ft$ and length is $6$ $ft$ of the rectangular mat.

Explanation of Solution

Given:

Length of rectangular mat is twice the width.

  

Formula Used:

Area of a rectangle $=$ length $\times$ Breadth

Calculation:

Given:

Length of rectangular mat is twice the width.

Let the width be $x$$ft$

Thus, Length $=$$2x$$ft$

Area of one rectangular mat is $18f{t}^2$

Thus, Area of one rectangular $=$$2x\times x$

  $2x\times x=18$

  $\begin{array}{l}{x}^2=9\\ x=3\end{array}$

Thus, the width be $3$$ft$

And, Length $=$$2\times 3$$ft$

Length $=$$6$$ft$

Conclusion:

Hence, the width is $3$$ft$ and length is $6$$ft$ of the rectangular mat.