Chapter 8.2, Problem 43PPS

a.

To determine

To determine the area expression of the tennis court.

Answer to Problem 43PPS

  $1.5x^2+24x$ square feet

Explanation of Solution

Given:

  

Length of the court $=1.5x+24$

Width of the court $=x$

Formula used:

Area of rectangle $=$ length $\times$ width

Calculation:

Length of the court $=1.5x+24$

Width of the court $=x$

  $\Rightarrow$ Area of tennis court $=$ length $\times$ width

  $\Rightarrow$ Area of tennis court $=(1.5x+24)(x)$

  $\Rightarrow$ Area of tennis court $=1.5x^2+24x$ square feet

Conclusion:

Therefore, the area expression of the tennis court is $1.5x^2+24x$ square feet.

b.

To determine

To determine the area expression of the path

Answer to Problem 43PPS

  $x^2-9x$ square feet

Explanation of Solution

Given:

  

Length of the path $=2.5x$

Width of the court $=x+6$

Formula used:

Area of rectangle $=$ length $\times$ width

Calculation:

Length of the path $=2.5x$

Width of the court $=x+6$

  $\Rightarrow$ Area of total rectangle $=$ length $\times$ width

  $\Rightarrow$ Area of total rectangle $=(2.5x)(x+6)$

  $\Rightarrow$ Area of total rectangle $=2.5x^2+15x$ square feet

Now, Area of the path $=$ Area of total rectangle $-$ Area of tennis court

  $\Rightarrow$ Area of the path $=$ Area of total rectangle $-$ Area of tennis court

  $\Rightarrow$ Area of the path $=$ $2.5x^2+15x$ $-$ $1.5x^2-24x$

  $\Rightarrow$ Area of the path $=$ $x^2-9x$ square feet

Conclusion:

Therefore, the area expression of the path is $x^2-9x$ square feet.

c.

To determine

To determine the perimeter of the outside the path

Answer to Problem 43PPS

  $264$ feet

Explanation of Solution

Given:

  

Length of the path $=2.5x$

Width of the court $=x+6$

Formula used:

Perimeter of rectangle $=2\times (\text{length+width)}$

Calculation:

Length of the path $=2.5x$

Width of the court $=x+6$

  $\Rightarrow$ Perimeter of rectangle $=2\times (\text{length+width)}$

  $\Rightarrow$ Perimeter of rectangle $=2\times (2.5x+x+6)$

  $\Rightarrow$ Perimeter of rectangle $=7x+12$

Now, $x=36$ feet

  $\Rightarrow$ Perimeter of rectangle $=7\times 36+12$

  $\Rightarrow$ Perimeter of rectangle $=264$ feet

Conclusion:

Therefore, the perimeter of the outside the path when $x=36$ feet is $264$ feet.