My Math Forum (http://mymathforum.com/math-forums.php)
-   Algebra (http://mymathforum.com/algebra/)
-   -   Border Question - Urgent (http://mymathforum.com/algebra/41048-border-question-urgent.html)

 helpmeplease12 January 26th, 2014 05:10 PM

Border Question - Urgent

A rectangular lawn measures 7m by 5 m. A uniform border of flowers is to be planted along !!!2!!! adjacent sides of the lawn, as shown in the diagram. If the flowers that have been purchased will cover an area of 6.25msquared, how wide is the border?

 soroban January 26th, 2014 05:46 PM

Re: Border Question - Urgent

Quote:
 A rectangular lawn measures 7m by 5 m. A uniform border of flowers is to be planted along two adjacent sides of the lawn. If the flowers that have been purchased will cover an area of 6.25 meters squared, how wide is the border?

Code:

      : - - 7 - - : x :     - *-----------*---*     : |          |:::|     5 |  lawn    |:::| x+5     : |          |:::|     - *-----------*:::|     x |:::::::::::::::|     - *---------------*             x+7
$\text{Total area: }\:(x\,+\,7)(x\,+\,5) \:=\:x^2\,+\,12x\,+\,35$

$\text{Lawn area: }\:7\,\times\,5\:=\:35$

$\text{Garden area: }\:(x^2\,+\,12x\,+\,35)\,-\,35 \:=\:x^2\,+\,12x$

$\text{Garden is 6.25\,m}^2:\;\;x^2\,+\,12x \:=\:6.25 \;\;\;\Rightarrow\;\;\;4x^2\,+\,48x \:=\:25$

[color=beige]. . . [/color]$4x^2\,+\,48x\,-\,25 \:=\:0 \;\;\;\Rightarrow\;\;\;(2x\,-\,1)(2x\,+\,25) \:=\:0$

$\text{Therefore: }\:x \,=\,\frac{1}{2}\,\text{m}$

 skipjack January 27th, 2014 01:18 PM

Quote:
 Originally Posted by soroban Garden is 6.25 m²: . . .
I assume you meant "Border" rather than "Garden".

 All times are GMT -8. The time now is 06:08 PM.