Mr. Santana wants to carpet exaxtly half of his rectangular living room. He knows that the perimeter of the room is 96 feet and that the length of the room is 6 feet longer than the width. How many square feet of carpeting does Mr. Santana need.

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- Jun 7th 2007, 10:48 AMaznmartinjaiCarpeting
Mr. Santana wants to carpet exaxtly half of his rectangular living room. He knows that the perimeter of the room is 96 feet and that the length of the room is 6 feet longer than the width. How many square feet of carpeting does Mr. Santana need.

- Jun 7th 2007, 12:20 PMearboth
Hello,

let l be the length of the room,

let w b the width of the room,

the perimeter of a rectangle is calculated by:

$\displaystyle p = 2 \cdot l + 2\cdot w$

You know: l - w = 6 that means l = w+6

$\displaystyle p = 96 = 2 \cdot (w+6) + 2\cdot w \ \Longleftrightarrow \ 96 = 4w + 12 \Longleftrightarrow w = 21$

Plug in this value to calculate the length: l = 27.

The area of a rectangle is calculated by:

$\displaystyle A_{rect} = l \cdot w \ \Longrightarrow A_{rect} = 21 \cdot 27 = 567$

I'll leave the rest for you :D