A rectangular Garden has an area of 132 m^2 and a perimeter of 46 m.

Questions:
1.) What equation would describe the area of the garden?
2.) What can you say about the equation formulated in item 1?
3.) Find the roots of equation formulated in item 1. What do the roots represent?
4.) What is the sum of the roots? How is this related to the perimeter?
5.) What is the product if the roots? How is this related to area?

PLEEEAASSSEE NEED ANSWER RIGHT AWAY.

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Answers

2014-11-24T19:11:11+08:00

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1.)132m²=lw
2.)I can say that the total area is 132m², and we have to find the unknown lengths and widths in the rectangular garden.
3)132m²=lw
    46m=2l+2w

132m²=lw
w=132m²/l

46m=2l+2(132/l)
l[46m=2l+264/l]
46l=2l²+264
0=2l²-46l+264
0=l²-23l+132
0=(l-12)(l-11)
l=12, l=11

132m²=lw
132m²=11w
w=12

132m²=lw
132m²=12w
w=11

4.The sum of the roots is 23, it is related to the perimeter because the perimeter's formula is twice the sum of the length and width if and only if it is a rectangle.

5.The product of the roots is 132, it is related to the area because the length is multiplied to the width in order to find the area, if and only if the shape is a rectangle.

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