ana is instructed to make a garden plot which has an area less than 18ft2 the length should be at 3ft longer than its width what are the possible dimensions of the box 1. how would you represent the width of the garden plot. 1) how would you represent the width of the garden plot 2)what would be the mathematical sentence 3)what are the possible dimensions of the garden plot
Answers
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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