SOLUTION: A rectangular corral built with 190 m of fencing that inludes four separate grazing areas lies on a 962 m(square) rectangular plot of land. the fence that divides the grazing areas

Question 106691: A rectangular corral built with 190 m of fencing that inludes four separate grazing areas lies on a 962 m(square) rectangular plot of land. the fence that divides the grazing areas is parallel to two of the sides of the corral. if there is a 1 m strip of land between each side of the corral and the property line, find the dimesions of the corral. there may be more than one answer!!...
Answer by edjones(7311) (Show Source):
You can put this solution on YOUR website!
L*w=A
2L+2w=P
.
L*w=926
Our 2nd formula uses the perimeter formula plus the extra fencing to divide the corral in quarters. We have to use 3 instead of 2 for the coeficients of L and w because of the extra fencing to divide the coral into 4ths. we also have to subtract 2 from L and w to account for the 1 m strip of land not used for the corral
3(L-2)+3(w-2)=190
3L-6+3w-6=190
3L+3w-12=190
3L+3w=190+12
3L+3w=202
.
A) L*w=926
B) 3L+3w=202
.
L=926/w
3(926/w)+3w=202 substitute 926/w for L
2778/w+3w=202
2778+3w^2=202w multiply each side by w to eliminate the fraction.
3w^2-202w+2778=0
Quadratic Formula (see below): w=19.26 m, w= 48.06
I made L= 48.06 m and w= 19.26 m
.
Ed

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=7468 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 48.0695984669789, 19.2637348663545. Here's your graph: