A determined gardener has 120 ft of fencing material. He wants to enclose a rectangular garden in his backyard, and wants an area that is enclosed to be at least 800 ft². What are the possible length of the garden?
(With solution po tenkyuu..)
(With solution po tenkyuu..)
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A square has the largest area for perimeter length.
120/4=30 length of a side of the square
30^2=900 ft^2 largest area.
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(30+x)(30-x)=800 Let x be the increase in length (or the decrease in width)
900-x^2=800
-x^2+100=0
x^2-100=0 multiply each side by -1
(x-10)(x+10)=0
x=10
40 x 20 is the longest 800 ft^2 area rectangle that can be built.
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The longest length is 40 ft and the shortest is 30 ft.
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