Let's address each part of the question step by step:
### Part (a)
Given:
- Perimeter of the rectangular parking lot = 366 meters
- Width of the parking lot = 85 meters
To find:
- Length of the parking lot
Solution:
The formula for the perimeter [tex]\( P \)[/tex] of a rectangle is given by:
[tex]\[ P = 2 \times (L + W) \][/tex]
where [tex]\( L \)[/tex] is the length and [tex]\( W \)[/tex] is the width.
Substitute the given values:
[tex]\[ 366 = 2 \times (L + 85) \][/tex]
First, divide both sides by 2 to isolate [tex]\( (L + 85) \)[/tex]:
[tex]\[ 183 = L + 85 \][/tex]
Next, subtract 85 from both sides to solve for [tex]\( L \)[/tex]:
[tex]\[ L = 183 - 85 \][/tex]
[tex]\[ L = 98 \][/tex]
So, the length of the parking lot is [tex]\( 98 \)[/tex] meters.
### Part (b)
Given:
- Area of the rectangular pool = 8256 square meters
- Length of the pool = 96 meters
To find:
- Width of the pool
Solution:
The formula for the area [tex]\( A \)[/tex] of a rectangle is given by:
[tex]\[ A = L \times W \][/tex]
where [tex]\( L \)[/tex] is the length and [tex]\( W \)[/tex] is the width.
Substitute the given values:
[tex]\[ 8256 = 96 \times W \][/tex]
To solve for [tex]\( W \)[/tex], divide both sides by 96:
[tex]\[ W = \frac{8256}{96} \][/tex]
[tex]\[ W = 86 \][/tex]
So, the width of the pool is [tex]\( 86 \)[/tex] meters.
### Summary:
(a) The length of the parking lot is 98 meters.
(b) The width of the pool is 86 meters.
