The amount by which the length and width of a shed can be increased to
more than double the area, depends on the initial dimensions.
- The amount that can be added to both the length and the width to increase the floor area by more than double the original area is more than <u>3 meters</u>.
Reasons:
The given parameters of the shed are;
The length of the shed = 12 m
Width of the shed = 5 m
The amount by which the length and the width are increased = The same amount
The new area after the increase in the length and width of the shed = More than double the initial area
Required:
The amount of increase in the length.
Solution:
Let the amount by which the length and width are increased = x
We have;
Initial area of the shed = 12 m × 5 m = 60 m²
The new area = (12 + x) × (5 + x) > 2 × 60
By multiplication, we get;
(12 + x) × (5 + x) = x² + 17·x + 60 > 2 × 60 = 120
x² + 17·x + 60 - 120 > 120 - 120 = 0
x² + 17·x - 60 > 0
By factorization, we get;
(x + 20)·(x - 3) > 0
x > -20, or x > 3
The increase (positive) amount of the solution is x > 3
Therefore, <u>the amount by which both the length and the width can be increased to more than double the area is x > 3 meters</u>
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