Jim wants to build a rectangular parking lot along a busy street but only has 1400 feet of fencing available.?

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thanks

Jim wants to build a rectangular parking lot along a busy street but only has 1400 feet of fencing available. If no fencing is required along the street, find the maximum area of the parking lot.

la console . it says your answer is wrong. maybe you forgot that their is no fencing along the street?

also it has to be a rectangle

• w: width of the parking

ℓ: length of the parking

The perimeter of the parking is the length of the fence:

2.(ℓ + w) = 1400

ℓ + w = 700

w = 700 – ℓ

The area of the parking is:

a = w * ℓ → you know that: w = 700 – ℓ

a = (700 – ℓ).ℓ

a = 700ℓ – ℓ² ← this is a function of ℓ

You can get the maximum of a function when its derivative is null.

a’ = 700 – 2ℓ → then you solve the equation: a’ = 0

700 – 2ℓ = 0

2ℓ = 700

→ ℓ = 350

Recall: w = 700 – ℓ → w = 700 – 350 → w = 350

You can see that: ℓ = w = 350

So the maximum of the area of the parking is when the parking is a square.

The area is: 350 * 350 = 122 500 ft²

• It might be possible for sure

• And?

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