SOLUTION: a rectangle garden measuring 80 by 60 meters has its area doubled by a border of uniform width along on both shorter sides and one longer sides. find the width of the border.
Algebra ->
Customizable Word Problem Solvers
-> Numbers
-> SOLUTION: a rectangle garden measuring 80 by 60 meters has its area doubled by a border of uniform width along on both shorter sides and one longer sides. find the width of the border.
Log On
Question 1121770: a rectangle garden measuring 80 by 60 meters has its area doubled by a border of uniform width along on both shorter sides and one longer sides. find the width of the border. Found 2 solutions by ankor@dixie-net.com, solver91311:Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! a rectangle garden measuring 80 by 60 meters has its area doubled by a border of uniform width along on both shorter sides and one longer sides.
find the width of the border.
:
let x = the width of the border
:
The overall dimensions, including the border, (x+80) by (2x+60)
The area including the border 2(80*60) = 9600 sq/ft
the area equation
(x+80)(2x+60) = 9600
FOIL
2x^2 + 60x + 160x + 4800 = 9600
2x^2 + 220x + 4800 - 9600 = 0
2x^2 + 220x - 4800 = 0
simplify, divide by 2
x^2 + 110x - 2400 = 0
Use the quadratic formula; a=1; b=110; c = -2400
the positive solution
x = 18.6546 ft, or about 18 ft 8 inches is the width of the border
:
:
See if that checks out
(18.6546+80) * (2(18.6546)+60)
98.6546 * 97.3092 = 9600.00 sq/ft, twice the original area
Put the quadratic into standard form then solve for . Note: You will get two roots to the quadratic, one will be positive and the other negative. Which one do you suppose is the correct one?
John
My calculator said it, I believe it, that settles it
