High School

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1.1.1 Define the term "Perimeter" in the given context.

1.1.2 Determine the length of the tennis court in miles, and round your answer to four decimal places.

1.1.3 Convert the length and the width of the tennis court to meters.

1.1.4 Calculate the perimeter of the tennis court in yards.
You may use the following formula:
\[ \text{Perimeter} = 2(\text{Length} + \text{Width}) \]

1.1.5 The temperature on one of the match days was 22°C. Convert the temperature to the nearest 5°F.
You may use the following formula:
\[ °C = \frac{(F-32) \times 5}{9} \]

1.1.6 Calculate the area of the backcourt in square feet (ft²).

**Diagram of the Tennis Court with Dimensions:**

| Feature | Measurement |
|--------------------------|----------------------|
| Baseline | Net (3 FT. HIGH) |
| | 78 FT. |
| Doubles Alley | Center Mark |
| | Service Line |
| Ad Court Service Box | 21 FT. |
| Deuce Court Service Box | |
| | 13.5 FT |
| Singles Sideline | Doubles Sideline |
| | 18 FT. |
| | 4.5 FT. |
| Doubles - 36 FT. | |
| | 3 FT. |
| Backcourt Center Service Line |

**Conversion Notes:**
- 1 ft = 0.3048 m
- 1 inch = 2.54 cm

**Length Conversion Chart:**
- Mile → Yard (* 1760)
- Yard → Feet (* 3)
- Feet → Inch (* 12)

Answer :

1.1.1 Definition of Perimeter:

The perimeter of a shape is the total distance around its edges or boundaries. In the context of a rectangle (like a tennis court), it's calculated by adding the lengths of all the sides together, or using the formula [tex]P = 2(l + w)[/tex], where [tex]l[/tex] is the length and [tex]w[/tex] is the width.

1.1.2 Determine the length of the tennis court in miles:

  • The length of the tennis court is given as 78 feet.
  • To convert feet to miles, use the conversion 1 mile = 5280 feet.

[tex]\text{Length in miles} = \frac{78}{5280} = 0.0148 \text{ miles}[/tex]

Rounding to 4 decimal places, the length is 0.0148 miles.

1.1.3 Convert the length and the width of the tennis court to metres:

  • 1 foot = 0.3048 metres.
  • Length in metres: [tex]78 \text{ ft} \times 0.3048 = 23.7744 \text{ m}[/tex]
  • Width in metres (doubles court): [tex]36 \text{ ft} \times 0.3048 = 10.9728 \text{ m}[/tex]

1.1.4 Calculate the perimeter of the tennis court in yards:

  • Length of the court is 78 feet; width for doubles is 36 feet.
  • Convert feet to yards (1 yard = 3 feet):

[tex]\text{Length in yards} = \frac{78}{3} = 26 \text{ yards}[/tex]
[tex]\text{Width in yards} = \frac{36}{3} = 12 \text{ yards}[/tex]

  • Using the perimeter formula:

[tex]\text{Perimeter} = 2(26 + 12) = 2 \times 38 = 76 \text{ yards}[/tex]

1.1.5 Convert the temperature to the nearest 5°F:

  • Given formula: [tex]\text{°C} = (\text{F} - 32) \cdot \frac{5}{9}[/tex]
  • We rearrange to solve for F:

[tex]\text{F} = \text{°C} \cdot \frac{9}{5} + 32[/tex]

  • [tex]\text{F} = 22 \cdot \frac{9}{5} + 32 = 71.6° \text{F}[/tex]
  • Rounding to the nearest 5, the temperature is 70°F.

1.1.6 Calculate the area of the backcourt in ft²:

  • The backcourt is typically calculated from the baseline to the service line (21 ft) and the width of the singles sideline (18 ft).

[tex]\text{Area} = 21 \text{ ft} \times 18 \text{ ft} = 378 \text{ ft}^2[/tex]

This calculated perimeter and area will help you understand not just the size of a tennis court but also conversion techniques across different units.

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Rewritten by : Barada