6.) a kennel owner has 168 feet of fencing with which
to enclose a rectangular region. he wants to subdivide
this region into three smaller rectangles of equal
length. if the total area to be enclosed 832 ft-, what are
the possible dimensions of the region?

The possible dimensions of the region are

52 ft by 16 ft

32 ft by 26 ft

Step-by-step explanation:

Let

x -----> the length of the rectangular region

y ----> the width of the rectangular region

we know that

The perimeter of a rectangle is equal to

Remember that

A kennel owner wants to subdivide  this region into three smaller rectangles of equal  length

so

we also have to take into account the divisions

we have

simplify

-----> -----> equation A

The total area to be enclosed is 832 ft^2

The area is equal to

so

----> equation B

substitute equation A in equation B

Solve the quadratic equation by graphing

The solution are y1=16 ft, y2=26 ft

see the attached figure

For

For

therefore

The possible dimensions of the region are

52 ft by 16 ft

32 ft by 26 ft