Chapter 6, Problem 7PT

To determine

Tofind:The length and width of a garden whose perimeter is given, by setting the equations defining the variables and solving equations by using substitution.

Answer to Problem 7PT

The length and width of the garden are 15 feet and 6 feet respectively.

Explanation of Solution

Given information:

The perimeter of Corey rectangular garden is 42 feet, and its length is equal to the width minus 3 feet.

Corey’s Garden $\to$   

Formulaused:

The perimeter of a rectangle is given by $P\text{=2×}\left(\text{length+width}\right)$

Calculations:

Suppose the length and width of the garden are x, and y respectively. Then the perimeter of the garden is $P\text{=2×}\left(x\text{+}y\right)$ . But perimeter of the garden is 42 feet. Therefore, $\text{2×}\left(x\text{+}y\right)=42$

  $x+y=\frac{42}{2}=21$  ...(1)

Further, thelength of garden is equal to the width minus 3 feet, i.e.,

  $x=3y-3$  ...(2)

The equations (1) and (2) describe the garden.

Now, substituting $x=3y-3$ in equation (1)

  $\left(3y-3\right)+y=21$

  $\Rightarrow 4y-3=21$

  $\Rightarrow 4y=21+3=24$

  $\Rightarrow y=\frac{24}{4}=6$

As, $x=3y-3$

  $\Rightarrow x=3\cdot 6-3=15$

Thus, the length and width of the garden are 15 feet and 6 feet respectively.

Conclusion:

The length and width of the garden are 15 feet and 6 feet respectively.