The Parkhursts used 160 yd of fencing to enclose a rectangular corral 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 ( yd has a small 2 above the d)
SO CONFUSED NEED TO SHOW STEPS
2 answers
I answered this already
The the width be x yds
let the length be y yds
then 3x + 2y = 160
y = (160-3x)/2
area = xy
x(160-3x)/2 = 1000
160x - 3x^2 = 2000
3x^2 - 160x + 2000 = 0
(x-20)(3x - 100)= 0
x = 20 or x= 100/3
if x=20, then y = 50
if x=100/3 then y = 30
Case 1, x=20, y =50
3(20) + 2(50) = 160, area = 20*50 = 1000
Case 2 x = 100/3, y =30
3(100/3) + 2(30) = 160, area = 30*100/3 = 1000
So the dimensions could be 20 by 50, with the third side parallel to the 20
or
the dimensions could be 100/3 by 30 with the third side parallel to the 100/3 side.
let the length be y yds
then 3x + 2y = 160
y = (160-3x)/2
area = xy
x(160-3x)/2 = 1000
160x - 3x^2 = 2000
3x^2 - 160x + 2000 = 0
(x-20)(3x - 100)= 0
x = 20 or x= 100/3
if x=20, then y = 50
if x=100/3 then y = 30
Case 1, x=20, y =50
3(20) + 2(50) = 160, area = 20*50 = 1000
Case 2 x = 100/3, y =30
3(100/3) + 2(30) = 160, area = 30*100/3 = 1000
So the dimensions could be 20 by 50, with the third side parallel to the 20
or
the dimensions could be 100/3 by 30 with the third side parallel to the 100/3 side.
1 answer