Asked by Laura
A GARDENER HAS 60' of edging. She wants to use it to enclose a 120 square foot rectangular area. She does not have to use up all of the edging. what are the possible lengths that a side of the rectangle can have? Answer using interval notation. Hint: if the length of the rectangle is x, and the area is 120, what is the width?
Answers
Answered by
Steve
x+y <= 60
xy = 120
so,
x + 120/x <= 60
x^2 + 120 <= 60x
x^2 - 60x + 120 <= 0
The two roots of this equation are
x = [60±√(3600-480)]/2 = 30±2√195
since this is a parabola which open up, it is negative between the roots. so,
x ∊ [30-2√195,30+2√195]
xy = 120
so,
x + 120/x <= 60
x^2 + 120 <= 60x
x^2 - 60x + 120 <= 0
The two roots of this equation are
x = [60±√(3600-480)]/2 = 30±2√195
since this is a parabola which open up, it is negative between the roots. so,
x ∊ [30-2√195,30+2√195]
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