dens. The gardener wants the enclosed area to be 286 square meters.

Mathematics
Tutor: None Selected Time limit: 1 Day

A gardener has 100 meters of fencing .The gardener wants the enclosed area to be 286 square meters.

4x+3y=100

Mar 8th, 2015

Two rectangle areas =286

The fence will have width 3 times and length 4 times .

Each rectangle area= xy

2xy =286

xy =143

4x+3y =100

4xy = 572

(100-3y)y =572

3y2-100y+572=0

3y2 -78y-22y+572=0

3y(y-26)-22(y-26)=0

(y-26)(3y-22)=0

Y =26 or y =22/3

If y =26  then 4x = 100-78 =22  ;  x =5.5

If y =22/3  then  4x =100-22=78  ; x=19.5

Both the solutions are possible

If you want length larger then x =19.5 y =22/3

x= 19.5  m  y =22/3 m

or

x=5.5  m y=26 m


Mar 8th, 2015

I'm a little confused I see you have a fraction and are the numbers rounded or no?

Larger x value:

Smaller x value:

Mar 8th, 2015

yes y =22/3 ; 3y =22 

x =19.5 4x =78

4x+3y =100

or

x = 5.5 

4x =22

y =26

3y =78

4x+3y =100 again

In both cases

xy = 5.5 *26 = 11*13 =143 or

xy =19.5 *22/3 = 6.5*22 = 13*11 =143

Both will fit the answer. Fractions get eliminated

Mar 8th, 2015

I can give the process and the exact answers. To prevent outside help they may feed the answers in a particular fashion and provide you dynamic prompting. That is why , I refrain from answering questions for computer evaluation


Mar 8th, 2015

Larger x value is 19.5     ;      4x=78

smaller x value is 5.5    ;        4x=22

Larger y value is 26     ;          3y =78

smaller y value is 22/3  ;         3y =22

But I do not know how you are prompted to enter fractions.

Mar 8th, 2015

This is the reason I do not want to answer computer evaluated ones.

You should watch the prompt whether to enter 19.5 or 19 1/2 or 39/2 for larger x value

Similarly for smaller x value it may be 5.5 or 5 1/2 or 11/2

Mar 8th, 2015

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