We appreciate your visit to A gardener has 97 feet of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it If. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To solve the problem of finding the dimensions of the garden and its area, we need to take into account the total fencing available and the width of the border. Let's walk through the solution step by step.
1. Understanding the Total Fencing:
The gardener has 97 feet of fencing to enclose a rectangular garden that has a 2-feet wide border surrounding it. Given that the length and width of the garden are the same, we know it's a square garden.
2. Calculating the Outer Perimeter:
Since the garden is square and has a border, the total length of fencing available (97 feet) must enclose the outer perimeter, including the border. Let's denote the side length of the square garden as [tex]\( s \)[/tex]. The outer side length, including the 2-feet border on each side, is [tex]\( s + 4 \)[/tex] feet.
3. Forming the Equation:
The perimeter of the outer square (including the border) is:
[tex]\[
4 \times (s + 4) = 97
\][/tex]
4. Solving for [tex]\( s \)[/tex]:
[tex]\[
s + 4 = \frac{97}{4}
\][/tex]
[tex]\[
s + 4 = 24.25
\][/tex]
[tex]\[
s = 24.25 - 4
\][/tex]
[tex]\[
s = 20.25
\][/tex]
5. Calculating the Area of the Garden:
The side length of the garden without the border is 20.2 feet (rounded to the nearest tenth). To find the area of the square garden:
[tex]\[
\text{Area} = (s)^2 = (20.2)^2 = 20.2 \times 20.2 = 410.0
\][/tex]
Notice in the final rounded form:
[tex]\[
\text{Area} = 410.1 \text{ square feet}
\][/tex]
Thus, the dimensions of the garden are 20.2 feet by 20.2 feet, and the area is 410.1 square feet.
1. Understanding the Total Fencing:
The gardener has 97 feet of fencing to enclose a rectangular garden that has a 2-feet wide border surrounding it. Given that the length and width of the garden are the same, we know it's a square garden.
2. Calculating the Outer Perimeter:
Since the garden is square and has a border, the total length of fencing available (97 feet) must enclose the outer perimeter, including the border. Let's denote the side length of the square garden as [tex]\( s \)[/tex]. The outer side length, including the 2-feet border on each side, is [tex]\( s + 4 \)[/tex] feet.
3. Forming the Equation:
The perimeter of the outer square (including the border) is:
[tex]\[
4 \times (s + 4) = 97
\][/tex]
4. Solving for [tex]\( s \)[/tex]:
[tex]\[
s + 4 = \frac{97}{4}
\][/tex]
[tex]\[
s + 4 = 24.25
\][/tex]
[tex]\[
s = 24.25 - 4
\][/tex]
[tex]\[
s = 20.25
\][/tex]
5. Calculating the Area of the Garden:
The side length of the garden without the border is 20.2 feet (rounded to the nearest tenth). To find the area of the square garden:
[tex]\[
\text{Area} = (s)^2 = (20.2)^2 = 20.2 \times 20.2 = 410.0
\][/tex]
Notice in the final rounded form:
[tex]\[
\text{Area} = 410.1 \text{ square feet}
\][/tex]
Thus, the dimensions of the garden are 20.2 feet by 20.2 feet, and the area is 410.1 square feet.
Thanks for taking the time to read A gardener has 97 feet of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it If. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
Answer:Let's break this problem down step by step!
1. The gardener has 97 feet of fencing, and the border is 2 feet wide, so we need to subtract 4 feet (2 feet x 2 sides) from the total fencing to get the actual perimeter of the garden: 97 - 4 = 93 feet.
2. Since the garden is square (length = width), we can divide the perimeter by 4 to get the length of one side: 93 ÷ 4 = 23.25 feet (round to 23.3 feet).
3. Now, we need to subtract the border width (2 feet) from the length of one side to get the actual length of the garden: 23.3 - 2 = 21.3 feet.
4. Since the garden is square, the width is the same as the length: 21.3 feet.
5. Finally, we can calculate the area of the garden: Area = Length x Width = 21.3 x 21.3 = 454.89 square feet (round to 454.9 square feet).
So, the dimensions of the garden are approximately 21.3 feet x 21.3 feet, and the area is approximately 454.9 square feet.
Step-by-step explanation:
