ana needs to make a garden plot which has an area less than 18ft². the length should be 3ft longer than the width. what are the possible dimensions of the box?
Answers
Answer:
Maximum length = 6ft
Maximum width = 3ft
Step-by-step explanation :
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Given : a garden plot which has an area less than 18 ft²
length should be at 3ft longer than its width
To Find : what are the possible dimensions
Solution:
Let say Width = w ft
Length = w + 3 ft
Area = Length x Width
=> area = (w + 3) w
=> area = w² + 3w
w² + 3w < 18
=> w² + 3w - 18 < 0
=> w² + 6w - 3w - 18 < 0
=> w(w + 6) - 3(w + 6) < 0
=> (w - 3)(w + 6) < 0
=> - 6 < w < 3
but width can not be negative
Hence 0 < w < 3
width of the garden plot. 0 < w < 3
width = 1 ft Length = 4 ft Area = 4 ft²
width = 2 ft Length = 5 ft Area = 10 ft²
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