SOLUTION: Translate the following into a quadratic equation, and solve it: The length of a rectangular garden is three times its width; if the area of the garden is 75 square meters, what

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Translate the following into a quadratic equation, and solve it: The length of a rectangular garden is three times its width; if the area of the garden is 75 square meters, what       Log On


   

Question 35900: Translate the following into a quadratic equation, and solve it:
The length of a rectangular garden is three times its width; if the area of the garden is 75 square meters, what are its dimensions?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the formula for the area of a rectangle:A+=+L%2AW
In your problem, L = 3W...substitute this into the basic formula.
A+=+%283W%29%2AW
A+=+3W%5E2 But the area (A) is given as 75 square meters.
75+=+3W%5E2 Subtract 75 from both sides.
3W%5E2-75+=+0 There's the quadratic equation.
To solve, factor out a 3.
3%28W%5E2-25%29+=+0Apply the zero products principle.
W%5E2-25+=+0 Solve by factoring.
%28W-5%29%28W%2B5%29+=+0 Apply the zero products principle.
W-5+=+0 and/or W%2B5+=+0
If W-5+=+0 then W+=+5 This is an acceptable solution since W is positive.
If W%2B5+=+0 then W+=+-5 This is not meaningful as the width, W, must be a positive value.
The width (W) is 5 meters.
The length (L) is 3W = 3(5) = 15 meters.