Pregunta
Solve the following equation. Express your answer as an integer, simplified fraction, or decimal rounded to two decimal places. A rectangular-shaped parking lot is to have a perimeter of 624 yards. If the width must be 140 yards because of a building code, what will the length need to be?
Ask by Frank Collins. in Mexico
Mar 14,2025
Solución de inteligencia artificial de Upstudy
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The length of the parking lot needs to be 172 yards.
Solución
Solve the equation \( 2w+2l=624 \).
Solve the equation by following steps:
- step0: Solve for \(l\):
\(2w+2l=624\)
- step1: Move the expression to the right side:
\(2l=624-2w\)
- step2: Divide both sides:
\(\frac{2l}{2}=\frac{624-2w}{2}\)
- step3: Divide the numbers:
\(l=312-w\)
The equation \(2w+2l=624\) can be simplified to \(l=312-w\).
Given that the width must be 140 yards, we can substitute \(w=140\) into the equation to find the length:
\[l=312-140=172\]
Therefore, the length of the parking lot needs to be 172 yards.
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Simplifique esta solución Bonus Knowledge
To find the length of the parking lot, we can use the formula for the perimeter of a rectangle, which is P = 2L + 2W, where L is the length and W is the width. Given that the perimeter (P) is 624 yards and the width (W) is 140 yards, we can rearrange the formula. First, substitute the width into the formula: 624 = 2L + 2(140). Now simplify the equation: 624 = 2L + 280. Next, subtract 280 from both sides: 624 - 280 = 2L, 344 = 2L. Finally, divide by 2 to find the length: L = 344 / 2 = 172 yards. So, the length of the parking lot needs to be 172 yards.
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