# Math

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A gardener wants to fence the largest possible rectangular area using 200 yards of fencing. Find the best length and width of the garden.

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The largest area is a square.

P = 4S
200/4 = S

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even if it said rectangular?

so its's 50 yd by 50 yd?

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I also need help on this question:
Sandra walked to the top of a hill at a speed of 2km/h, turned around and walked down the hill at a rate of 4km/h. The whole trip took 6 hoours. How many kilometers is it to the top of the hill?

I thought it might be 6km but my math teacher checked it and said it wasn't.

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hello?Ms. Sue????

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A square is a rectangle. Yes. The largest area would be a square measuring 50 yards on each side.

Her average speed is 3 km/hour.

(3 * 6)/2 = ?

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W=Width

L=Length

P=Perimeter

A=Area

P=2(W+L)

200=2(W+L) Divide with 2

100=W+L

100-L=W

W=100-L

A=W*L=(100-L)*L

A=100L-L^2

dA/dL=100-2L

Function has minimum or maximum when first derivate=0

100-2L=0

100=2L Divide with 2

50=L

L=50 yd

If second derivate<0 then function has a maximum.

If second derivate>0 then function has a minimum.

Second derivate=-2<0
function has a maximum for L=50 yd

W=100-L

W=100-50=50 yd

A(max)=50*50=2500 yd^2

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what do you do with (*)

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* is sign for multiply