Mrs. Reyna is planning to fence her vacant lot for a parking space. The desired length of the lot is 10 meters longer than its width. What will be the possible dimensions of the rectangular parking space if it should be less than 80 sqm? (Hint: lengthx width = Area of rectangle)
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Possible dimensions,
Width = (0 , 4) or length - 6
Length = (6 , 10) or width + 6
Step-by-step explanation:
Let, width = x
length = x + 6
area < 40 m²
Solve,
Area = Length x Width
40 > (x + 6) x
40 > x² + 6x
0 > x² + 6x - 40
Rearrange and Factor,
(x + 10) (x - 4) < 0
Solve the inequalities,
x + 10 < 0
x1 < -10
x - 4 < 0
x2 < 4
Therefore, x (-10 , 4) = width
Length = x + 6
length = ( -4 , 10)
Since we're dealing with measurements, we disregard the negative values.
Width = (0 , 4)
Length = (6 , 10)