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Neporo4naja [7]
2 years ago
6

The area of a door is 3024 square inches. If the length of the door is 48 inches longer than the width of the door, what is the

width of the door?​
Mathematics
1 answer:
borishaifa [10]2 years ago
7 0

Answer:

The width of the door is 36 inches

Step-by-step explanation:

The given parameters are;

The given area of the door = 3024 in.²

The length of the door = 48 + The width of the door

Let W represent the width of the door

Therefore, we have;

The length of the door = 48 + W

The area of the door = The length of the door × The width of the door

∴ By substitution, the area of the door = 3024 = W × (48 + W)

3024 = W × (48 + W) = 48·W + W²

48·W + W² = 3024

∴ 48·W + W² - 3024 = 0

Rearranging, we get;

W² + 48·W - 3024 = 0

By trial and error, we have;

(W + 84)×(W - 36) = 0

Therefore, given that the width of the door is a natural number, we have;

The width of the door, W = 36 inches

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