You have 200 ft of fencing to enclose two adjacent rectangular corrals. The total area of the enclosed region is 1400 sq ft. What are the dimensions of each corral? (The corrals are the same size)

Question

The two corrals share one of its widths, so there are only 3 widths, not 4. I can't figure this question out and I need to turn it in by tomorrow, please help me.

Answer 1

Area = 1400 = xy

y = 1400/x

200 feet = 2x +3y = 2x +3(1400/x) = 2x +4200/x = 200

multiply by x

2x^2 -200x= -4200

divide by 2

x^2 -100x =-2100

complete the square

x^2 -100x +2500 = -2100+2500 =400

(x-50)^2 = 400

x-50 = +/-20

x = 50+/-20 = 70 or 30

y=1400/70 = 20 or 1400/30 = 140/3 = 46 2/3

2x +3y = 140+60 = 200 or 60+140=200

area of each corral = 20(70) = 1400 or (140/3)(30) =1400

Answer 2

Let L = and W = width.

2L + 3W = 200

So, W = (200 - 2L) / 3

Area of each corral = (1/2)LW = (1/2)(L)(200 - 2L)/3 = (1/3)(100L - L²) = 700.

So, L² - 100L + 2100 = 0

(L - 30)(L - 70) = 0

L = 30 or 70

If L = 30, then W = 140/3 = 46.666

If L = 70, then W = 20

Each corral is either 35ft by 20ft or 15ft by 46.666ft