A city park commission received a donation of playground equipment from a parents' organization. The area of the playground needs to be 256 square yards for the children to use it safely. The playground will be rectangular.
A city park commission received a donation of playground equipment from a parents' organization. The area of the playground needs to be 256 square yards for the children to use it safely. The playground will be rectangular.
Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter10: Quadratic Equations
Section10.4: Solve Applications Modeled By Quadratic Equations
Problem 160E: A city planner wants to build a bridge across a lake in a park. To find the length of the bridge, he...
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![### Playground Perimeter Calculation
A city park commission received a donation of playground equipment from a parents' organization. The area of the playground needs to be 256 square yards for the children to use it safely. The playground will be rectangular.
The city will also put a fence around the playground. The perimeter, \( P \), of the fence includes the gates. To save money, the city wants the least perimeter of fencing for the area of 256 square yards.
With one side 8 yards longer than the other side, what are the side lengths for the least perimeter of fencing?
**Solution:**
\[ \text{side 1: } \_\_\_\_ \text{ yards} \]
\[ \text{side 2: } \_\_\_\_ \text{ yards} \]
**Buttons:**
- Submit Answer
- Ask for Help
- Turn It In
**Notes:**
- Ensure you calculate the dimensions correctly.
- The length and width should satisfy the area condition \( \text{length} \times \text{width} = 256 \) square yards.
- Consider the given that one side is 8 yards longer than the other.
### How to Calculate the Dimensions:
1. Let the width of the rectangle be \( x \) yards.
2. Then, the length of the rectangle will be \( x + 8 \) yards.
3. Using the area formula for a rectangle: \( \text{length} \times \text{width} = 256 \).
\[ (x + 8) \times x = 256 \]
\[ x^2 + 8x - 256 = 0 \]
4. Solve this quadratic equation to find \( x \).
Once \( x \) is found, \( x + 8 \) will provide the length.
These lengths will give the dimensions that provide the least perimeter for the specified area.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F127d94d1-728c-4c83-9222-f71e24ff3424%2Fd5a15818-11e2-4af4-84b2-9b04be498e32%2Foffbs5c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Playground Perimeter Calculation
A city park commission received a donation of playground equipment from a parents' organization. The area of the playground needs to be 256 square yards for the children to use it safely. The playground will be rectangular.
The city will also put a fence around the playground. The perimeter, \( P \), of the fence includes the gates. To save money, the city wants the least perimeter of fencing for the area of 256 square yards.
With one side 8 yards longer than the other side, what are the side lengths for the least perimeter of fencing?
**Solution:**
\[ \text{side 1: } \_\_\_\_ \text{ yards} \]
\[ \text{side 2: } \_\_\_\_ \text{ yards} \]
**Buttons:**
- Submit Answer
- Ask for Help
- Turn It In
**Notes:**
- Ensure you calculate the dimensions correctly.
- The length and width should satisfy the area condition \( \text{length} \times \text{width} = 256 \) square yards.
- Consider the given that one side is 8 yards longer than the other.
### How to Calculate the Dimensions:
1. Let the width of the rectangle be \( x \) yards.
2. Then, the length of the rectangle will be \( x + 8 \) yards.
3. Using the area formula for a rectangle: \( \text{length} \times \text{width} = 256 \).
\[ (x + 8) \times x = 256 \]
\[ x^2 + 8x - 256 = 0 \]
4. Solve this quadratic equation to find \( x \).
Once \( x \) is found, \( x + 8 \) will provide the length.
These lengths will give the dimensions that provide the least perimeter for the specified area.
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