Chapter 8.9, Problem 34E

(a)

To determine

To calculate: The area of kite A and kite B in square inches and then convert into square feet.

Answer to Problem 34E

Area of kite A $=2.375{\text{ ft}}^2$

Area of kite B $=3{\text{ ft}}^2$

Explanation of Solution

Given: A 48 square feet of paper to use making kites.Making two types of kites show below.

In kite A, there are two right triangle.

Now, find the area of both right triangle.

Area of kite $A=\frac{1}{2}\times 18\times 12+\frac{1}{2}\times 18\times 20$

Therefore, $A=342{\text{ in}}^2$

Now convert the area into square feet.

  $1{\text{ in}}^2=0.006944{\text{ ft}}^2$

So, Area of kite A in square feet $=342{\text{ in}}^2\times \frac{0.006944{\text{ ft}}^2}{1{\text{ in}}^2}=2.375{\text{ ft}}^2$

In kite B, there are two right triangles and one square.

Area of kite B = Area of triangle + Area of square

Therefore, Area of kite $B=2\times \frac{1}{2}\times 16\times 11+16\times 16=432{\text{ in}}^2$

Now convert the area into square feet.

  $1{\text{ in}}^2=0.006944{\text{ ft}}^2$

So, Area of kite A in square feet $=432{\text{ in}}^2\times \frac{0.006944{\text{ ft}}^2}{1{\text{ in}}^2}=3{\text{ ft}}^2$

(b)

To determine

To graph: The inequality which describing the number of kite A and kite B.

Answer to Problem 34E

Explanation of Solution

Given: A 48 square feet of paper to use making kites.Making two types of kites show below.

Area of kite A $=2.375{\text{ ft}}^2$

Area of kite B $=3{\text{ ft}}^2$

Let x number of kite A and y number of kite B formed.

Total area of paper is 48 square feet.

So, inequality form $2.375x+3y\le 48$

Now graph the inequality.

(C)

To determine

To analyze:The graph and points where all papers used.

Answer to Problem 34E

If both x and y are in integer then all paper used.

Either x or y is in decimal the paper left over.

Explanation of Solution

Given: A 48 square feet of paper to use making kites.Making two types of kites show below.

The graph of inequality and all integrals coordinate of x and y within feasible reason represents all paper used.

Either the value of x or y are in decimal which represents paper left over.