SOLUTION: Translate the following into a quadratic equation, and solve it: The length of a rectangular garden is four times its width; if the area of the garden is 196 square meters, what a

Algebra ->  Rectangles -> SOLUTION: Translate the following into a quadratic equation, and solve it: The length of a rectangular garden is four times its width; if the area of the garden is 196 square meters, what a      Log On


   

Question 186558: Translate the following into a quadratic equation, and solve it: The length of a rectangular garden is four times its width; if the area of the garden is 196 square meters, what are its dimensions?

Found 2 solutions by checkley77, Earlsdon:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
L=4W
LW=196
4W*W=196
4W^2=196
W^2=196/4
W^2=49
W=7 M IS THE WIDTH OF THE GARDEN.
L=4*7
L=28 M IS THE LENGTH OF THE GARDEN.
PROOF:
7*28=196
196=196

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 Substitute L+=+4%2AW "The length is four times the width."
A+=+4%2AW%2AW Substitute A = 196 "The area is 196 sq. meters."
4W%5E2+=+196 Subtract 196 from both sides.
4w%5E2-196+=+0 Divide both sides by 4.
W%5E2-49+=+0 This is the quadratic equation which can be solved by factoring.
%28W-7%29%28W%2B7%29+=+0 so that...
W+=+7 or W+=+-7 Discard the negative solution as the width is a positive quantity.
The width is 7 meters and the length is 4*7 = 28 meters.