A rectangular plot of land is to be enclosed by a fence. One side is along a river, and does not need to be enclosed. If the total available fencing is 600 meters, find the dimensions of the plot to have the maximum area

Width 150 meters.

Length = 350 meters.

Step-by-step explanation:

Let us assume the  width of  the fence = k meters

So, both sides = k + k = 2k meters

Also, the TOTAL fencing length = 600 m

So, the one side length of the fence = (600 - 2 k) meters

AREA = LENGTH x WIDTH

⇒ A(k)  = (600 - 2k) (k)

or, A =  -2k² + 600 k

The above equation is of the form: ax² +bx +  C

Here: a  = - 2 , b = 600 and C = 0

As a< 0, the parabola opens DOWNWARDS.

Here, x value is given as:  

Solving for the value of k similarly, we get:

Thus the desired width = k = 150 meters

So, the desired dimensions of the plot  is width 150 meters.

And length = 650 - 2k = 650 - 300 = 350 meters.

unless you made a typo, the answers are both a and c.

step-by-step explanation:

1.5/3 is .5 whereas 3/9 is .3333333 not proportional

22/33 is .66666 and 4/6 is also .66666 proportional

2/4 is .5 whereas 142/213 is .66666 not proportional

14/7 is 2 and 7/3.5 is also 2 proportional

you could've also checked it by doing this simple division:

if the larger fraction divides with the smaller fraction to equal 1, it is proportional. so let me show you what i mean:

when i divide 22/33 by 4/6 i get 1, so we know it is proportional, and it is the same with 14/7 and 7/3.5. now if i divide 3/9 by 1.5/3 i get .66666 so therefore we know it is not proportional.

there are many ways to do this so i wanted to show you some possible ways.