What is the range of this relation?
2 answers:
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Answer:
<em>Any width less than 3 feet</em>
Step-by-step explanation:
<u>Inequalities</u>
The garden plot will have an area of less than 18 square feet. If L is the length of the garden plot and W is the width, the area is calculated by:
A = L.W
The first condition can be written as follows:
LW < 18
The length should be 3 feet longer than the width, thus:
L = W + 3
Substituting in the inequality:
(W + 3)W < 18
Operating and rearranging:
Factoring:
(W-3)(W+6)<0
Since W must be positive, the only restriction comes from:
W - 3 < 0
Or, equivalently:
W < 3
Since:
L = W + 3
W = L - 3
This means:
L - 3 < 3
L < 6
The width should be less than 3 feet and therefore the length will be less than 6 feet.
If the measures are whole numbers, the possible dimensions of the garden plot are:
W = 1 ft, L = 4 ft
W = 2 ft, L = 5 ft
Another solution would be (for non-integer numbers):
W = 2.5 ft, L = 5.5 ft
There are infinitely many possible combinations for W and L as real numbers.