Chapter 1.6, Problem 3CYP

To determine

To calculate the shape of largest play area

Answer to Problem 3CYP

Square shaped play area

Explanation of Solution

Given information:

Total fencing Dasan has to fence 32 feet. Options for shape of play are are,

F. circle with radius 5 feet

G. rectangle with length 5 feet and width 10 feet

H. right triangle with legs 10 feet.

J. square with side 8 feet.

Formula used:

Circumference of circle,

  $circumference=2\pi r^{}$

  Perimeter of rectangle,

  $perimeter=2(w+l)$

  Perimeter of right-triangle,

  $perimeter=s_1^{}+s_2^{}+\sqrt{s_1^2+s_2^2}$

  Perimeter of square is,

  $perimeter=sumOfAllSides$

Calculation:

For circle, substituting the values,

  $circumference=2\times 3.14\times 5$

On solving,

  $circumference=31.4$

Hence, fence needed for circle play area is 31.4 feet

For rectangle, substituting the values,

  $perimeter=2(10+5)$

On solving,

  $perimeter=30$

Hence, fence needed for rectangle play area is 30 feet.

For triangle, substituting the values,

  $perimeter=10+10+\sqrt{{10}^2+{10}^2}$

So,

  $perimeter=20+14.14$

On solving,

  $perimeter=34.14$

Hence, fence needed for a right-triangle play area is 34.14 feet.

For square, substituting the sides,

  $perimeter=8+8+8+8$

On solving,

  $perimeter=32$

Hence, fence needed for a square play area is 32 feet.

The play shape with largest area is triangle shaped play area, but it requires more than the available fence. Hence, square is the largest shaped play area with uses all the fencing to fence.