Chapter 8.3, Problem 44PPE

(a)

To determine

To find: Equation of the dimension of pavilion.

Answer to Problem 44PPE

Length is 45ft and width is 15ft.

Explanation of Solution

Given information:

Length of pavilion is three times its width.

Around pavilion 3ft wide stone walk way is there.

Area of pavilion is 396ft²

Formula used:

  $area\text{ of rectangle}=\text{length}\times \text{width}$

Calculation:

  

Let the length of pavilion be y and width be x

As the walkaway width is 3ft

Length is $y+6$ and width is $y+6$

And $y=3x$

  $\begin{array}{l}area\text{ of walkaway}=\text{length}\times \text{width-Area of rectangle}\\ \text{A}=(\text{x}+\text{6)(y}+{\text{6)-3x}}^{\text{2}}\\ A=\text{(x}+\text{6)(3x}+{\text{6)-3x}}^{\text{2}}\\ 396=3x^2+24x+36-3x^2\\ 390=24x+36\\ 24x=360\\ x=15\\ \text{width}\text{is 15cm}\\ \text{and length is 3x }=\text{45cm}\end{array}$

Conclusion:

Length is 45ft and width is 15ft.

(b)

To determine

To find: Variable expression for the area of the walk away.

Answer to Problem 44PPE

Variable expression for the area of the walk away is $A=24x+36$

Explanation of Solution

Given information:

Length of pavilion is three times its width.

Around pavilion 3ft wide stone walk way is there.

Calculation:

The expression is:

  $\begin{array}{l}area\text{ of walkaway}=\text{length}\times \text{width-Area of rectangle}\\ \text{A}=(\text{x}+\text{6)(y}+{\text{6)-3x}}^{\text{2}}\\ A=\text{(x}+\text{6)(3x}+{\text{6)-3x}}^{\text{2}}\\ A=3x^2+24x+36-3x^2\\ A=24x+36\end{array}$

Conclusion:

Variable expression for the area of the walk away is $A=24x+36$