Rugs and Floors

[Guest]

rectangular rug

A rectangular rug covers half the floor area of a rectangular floor that is 9ft wide and 12 ft long.If the dimensions of the rug are in the same ratio of these floor,how long is the rug ?

my solution:

let rug length =x

x*9=9*12/2
x=6

but my book's answer is 6sqrt(2)

why i am wrong ? where is the mistake i have commited ?

 

[tkhunny]

I can't really tell what you are doing.

If x = rug length, then (9/12)x = rug width.

x*[(9/12)x] = (1/2)*(9*12)

 

[stapel]

Re: rectangular rug

x*9=9*12/2
x=6

Where did "9x = 9(12/2)" come from? How does it relate to the word problem?

Please reply with specifics. Thank you.

Eliz.

 

[soroban]

Re: rectangular rug

Hello, Anonymous!

Did you make a sketch?

A rectangular rug covers half the floor area of a rectangular floor that is 9ft wide and 12 ft long.
If the dimensions of the rug are in the same ratio as the floor, how long is the rug?

      * - - - - - - - - - *
      |                   |
      |   * - - - - - *   |
    9 |   |    4x     |   |
      |   |3x         |   |
      |   |           |   |
      |   * - - - - - *   |
      |                   |
      * - - - - - - - - - *
               12

The floor is 9 feet by 12 feet.
\(\displaystyle \;\;\)The ratio is \(\displaystyle 9:12\,=\,3:4\)

The rug's dimensions are in the same ratio (3:4)
\(\displaystyle \;\;\)The rug is \(\displaystyle 3x\) by \(\displaystyle 4x.\)

The rug's area \(\displaystyle (3x)(4x)\) is half of the area of the floor \(\displaystyle (9)(12)\)

There is our equation! . . . \(\displaystyle 12x^2\;=\;\frac{1}{2}(108)\)