SOLUTION: The Parkhursts used 160 yd of fencing to enclose a rectangular corral and to divide it into two parts by a fence parallel to one of the shorter sides. Find the dimensions of the co

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Question 198226: The Parkhursts used 160 yd of fencing to enclose a rectangular corral and to divide it into two parts by a fence parallel to one of the shorter sides. Find the dimensions of the corral if its area is 1000 yd^2.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The Parkhursts used 160 yd of fencing to enclose a rectangular corral and to
divide it into two parts by a fence parallel to one of the shorter sides.
Find the dimensions of the corral if its area is 1000 yd^2.
:
Let x = the width, the shorter side
Let L = the length
:
Perimeter for this configuration
2L + 3x = 160
L in terms of x
2L = 160 - 3x
divide both sides by 2
L = 80 - 1.5x
:
Area:
L * x = 1000
substitute (80-1.5x) for L
(80-1.5x) * x = 1000
A quadratic equation:
-1.5x^2 + 80x - 1000 = 0
Multiply by -2, change the signs, get rid of the decimal
3x^2 - 160x + 2000 = 0
Factors to:
(3x - 100)(x - 20) = 0
Two solutions
3x = 100
x = 331%2F3
and
x = 20 yd wide is the reasonable solution
:
Find the length
L = 80 - 1.5(20)
L = 80 - 30
L = 50 yds long
:
:
Check solution
2(50) + 3(20) = 160
and
50 * 20 = 1000 sq/yds