Maximum point question (1 Viewer)

[nazfiz]

A rectangular area is to be fenced and divided into six rectangles by one dividing fence parallel to its length and two fences parallel to its breadth. If the total length of fencing available is 120m, find the maximum possible area.

Can someone please answer this with working out
Thanks

 

[SpiralFlex]

First of all always draw a pretty diagram. I will let the length be and the breadth be



From our pretty diagram, in our breadth section. We can see one length is Similarly in our length section, one length is

Let's somehow related this. I know! We can use perimeter!

We have 4 breadths and only 3 lengths. So,





One equation generated. We obviously need more. Let's generate an equation for the area. We know the breadth is . We just generated an equation involving So we must know connect these two into an area format.





This I am sure you know where to go from here.



For maximum area or minimum area,



metres. Now we must test for maximum/minimum.



Clearly from our table a maximum area will occur when . So we can substitute this into our area formula.

 

[bleakarcher]

i got 300m^2 as well

 

[SpiralFlex]

i got 300m^2 as well

I must not be old after all.

 

[nazfiz]

Thanks guys. It was the generation of the equation part that had me stunned.