SOLUTION: A rectangular garden has an area of 84 sq meters and a perimeter of 38 meters. Find its length.

Question 982518: A rectangular garden has an area of 84 sq meters and a perimeter of 38 meters. Find its length.
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
.
L=length; W=width; A=Area; P=perimeter
.
P=2(L+W)
38m=2(L+W)
19m=L+W
19m-L=W
.
A=LW
84m^2=LW
84m^2=L(19m-L)
84m^2=19Lm-L^2
0=-L^2+19Lm-84m^2
0=L^2-19Lm+84m^2

Solved by pluggable solver: SOLVE quadratic equation with variable

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=25 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 12, 7. Here's your graph:

Length is 12 meters or 7 meters
(If length is 12m, width is 7m, if length is 7m width is 12m)
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