Chapter 1, Problem 35SGR

To determine

To find the areas of all three enclosure and determine which would provide the largest area

Answer to Problem 35SGR

Option 3 would provide the largest area

Explanation of Solution

Given information:

Westside Park received 440 ft. of chain link fencing as donation, park administrator wants maximum area, three options are

Option A- rectangle with 100 feet and width 120 feet

Option B − square with sides 110 feet

Option C- a circle with radius 70 feet

Formula used:

  Area of rectangle = $l\times b$

  Area of square = side $\times$ side

Area of circle = $\pi r^2$

Calculation: considering option A

Substituting values in the formula for rectangle

Area of rectangle = $100\times 120f{t}^2$

Solving further

Area = $12000f{t}^2$

Now considering option B

Substituting values in the formula for square

Area = $110\times 110$

Solving it further

Area = $12100f{t}^2$

Now, considering option C

Substituting values for the circle

Area = $\frac{22}{7}\times 70\times 70$

Solving it further

Area = $22\times 7\times 70=15400f{t}^2$

From the above option, option C would have the largest area which is $15400f{t}^2$