Mrs reyna is planning to fence her vacant space for a parking space. What will be the possible dimensions of the rectangular parking space if it should be less than 40 sqm?

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)