6. The length of a car park is 120 m longer than its width. The area of the car park is 6400 m².a. How would you represent the width of the car park?How about its length?b. What equation represents the area of the car park?C.How would you use the equation representing the area of the car park in finding itslength and width?d. What is the length of the car park? How about its width? Explain how you arrived at youranswer.e. Suppose the area of the car park is doubled, would its length and width also doubleJustify your answer.​

Step-by-step explanation:Let's break down the problem step-by-step: a. How would you represent the width of the car park? How about its length? - Width: Let's represent the width of the car park as "w".- Length: Since the length is 120 meters longer than the width, we can represent it as "w + 120". b. What equation represents the area of the car park? - The area of a rectangle (which a car park is assumed to be) is calculated by multiplying length and width.- So, the equation for the area of the car park is: Area = length * width- Substituting our representations from part (a), we get: 6400 = (w + 120) * w c. How would you use the equation representing the area of the car park in finding its length and width? - We have the equation: 6400 = (w + 120) * w- This is a quadratic equation. To solve for "w" (the width), we need to expand the equation, rearrange it, and then use the quadratic formula or factoring. d. What is the length of the car park? How about its width? Explain how you arrived at your answer. 1. Expand the equation: 6400 = w² + 120w2. Rearrange: 0 = w² + 120w - 64003. Solve for "w" using the quadratic formula:- w = (-b ± √(b² - 4ac)) / 2a- Where a = 1, b = 120, and c = -6400- Solving this, we get two possible values for "w": 40 and -160. Since width cannot be negative, we discard -160.4. Therefore, the width (w) is 40 meters.5. Calculate the length: Length = w + 120 = 40 + 120 = 160 meters e. Suppose the area of the car park is doubled, would its length and width also double? Justify your answer. - No, the length and width would not double if the area is doubled.- Justification: Area is calculated by multiplying length and width. If you double the area, you're essentially multiplying the original area by 2. To achieve this, you could either:- Double the length while keeping the width the same.- Double the width while keeping the length the same.- Increase both the length and width by a factor that, when multiplied together, equals 2. In conclusion: Doubling the area of a rectangle does not necessarily mean doubling both its length and width.HOPE IT HELPS YOU

Answered by december31mana | 2024-09-03