joyce wants to fence in a rectangular dog run in her backyard. she is going to use a total of 24 feet of fencing

Question

what is the width, w, of the dog run if it has an area 119 square feet ?

what is the width, w, of the dog run if it has an area of 135 square feet?

Answer 1

The formula for reverse area and perimeter is:

[G +or- sqrt ( G^2 - 4 * Area)] / 2 where G = perimeter/2

PROVIDED that perimeter >= 4 * sqrt(area)

BUT 4 * sqrt(area) = 4 * sqrt(119) > 24, so there is no such rectangle

that will fit.

Certainly a rectangle with an even LARGER area, yet same perimeter will

not fit either.

Answer 2

Part 1:

Area = Length x Width

119 = lw

You know she is only using 24ft of fencing. Therefore 2l + 2w = 24

Solve in terms of one variable.

2l = 24 - 2w

l = (24-2w)/2

l = 2(12 - w)/2

l = 12-w

Plug in for l

119 = lw

119 = (12-w)*w

119 = 12w - w^2

119-w^2 -12w = 0

-w^2 - 12w + 119 = 0

Solve the quadratic and get: w = -18.45 and 6.45. Since it's area ignore the negative answer and go with 6.45.

Now confirm and solve for length:

w=6.45

l=12-w = 12-6.45 = 5.55 ft

2l + 2w = 24

2(5.55) + 2(6.45) = 11.1 + 12.9 = 24 ft

Repeat for the second area. Good luck!