Chapter 1, Problem 13CT

(a)

To determine

To solve: the formula for $w$ .

Answer to Problem 13CT

the formula is $w$

  $\frac{1}{2}P-l=w$

Explanation of Solution

Given:

  

Calculation:

Solve for w:

Given equation

  $P=2l+2w$

Subtract $2l$ from both sides.

  $P-2l=2w$

Divide both sides by 2.

  $\frac{1}{2}P-l=w$

Conclusion:

the formula is $\frac{1}{2}P-l=w$

(b)

To determine

To find: the width of the field.

Answer to Problem 13CT

Width of the field is $65$ .

Explanation of Solution

Calculation:

Find the width of the field:

Substitute the perimeter and length into the equation.

  $\frac{1}{2}\left(330\right)-100=2$

Multiply.

  $165-100=w$

Subtract.

  $65=w$

Conclusion:

Width of the field is $65$ .

(c)

To determine

To find: the percent of the field inside the circle

Answer to Problem 13CT

The percent of the field inside the circle is $4.8\%$ percent

Explanation of Solution

Calculation:

Find the percentage of the field inside the circle:

Area formula for a circle is $A=\pi r^2$

Substitute the radius into the formula.

  $A=\pi \left({10}^2\right)$

Simplify.

  $A=100\pi$

Multiply.

  $A=314$

Area formula for a rectangle is $A=lw$

Substitute the length and width into the formula.

  $A=100\left(65\right)$

Multiply.

  $A=6500$

Divide the area of the circle by the area of the field.

  $\frac{314}{6500}$

Convert to a percent.

  $4.8\%$

Conclusion:

the percent of the field inside the circle is $4.8\%$ percent