Answer:
The answer is below
Step-by-step explanation:
vacant lot for a parking space. The desired length of the lot is 6 meters longer than its width. What will be the possible dimensions of the rectangular parking space if it should be less than 40sqm? (Hint: length x width = Area of rectangle).
Solution: Let l represent the length of the fence and w represent the width of the fence. Therefore:
l = w + 6
Area = Length × Width
Area = (w + 6) × w
Area = w² + 6w
The area of the rectangular space should be less than 40 sqm, hence:
w² + 6w < 40
w² + 6w - 40 < 0
w² + 10w - 4w - 40 < 0
w(w + 10) - 4(w + 10) < 0
(w - 4)(w + 10) < 0
w - 4< 0 or w + 10 < 0
w < 4 or w < -10
The width = (-10, 4)
The length = width + 6 = (-4, 10)
Since the width and length cannot be negative values hence:
Width = (0, 4), length = (6, 10)
