SOLUTION: The area of a rectangular room is 56 square feet. The length is 6 feet less than twice the width. Fin the dimensions of the room.

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Question 54292: The area of a rectangular room is 56 square feet. The length is 6 feet less than twice the width. Fin the dimensions of the room.
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
1. +A+=+LW+
2. +A+=+56+
3. +L+=+2w-6+
4. +W+=+W+
Substitute
+56+=+%282w-6%29%28w%29+
Distribute
+56+=+2w%5E2+-6w+
Subtract 56 from both sides
+0+=+2w%5E2+-6w+-56+
Simplify by dividing all parts by 2
+0+=+w%5E2+-3w+-28+
Factor
+0+=+%28w-7%29%28w%2B4%29+
Zero-Product Theorm ... ie: set each piece equal to zero
+0+=+w-7+ and +0+=+w%2B4+
+7=w+ and +-4=w+
NO WAY can a length be a negative number ... so -4 is out.
+W+=+7+


Go back to the equations 3 and 4 and plug in 7 for W
3. +L+=+2w-6+
+L+=+2%287%29+-6+
+L+=14+-+6
+L+=+8+
4. +W+=+W+
+W+=+7+
and since our Area is 56 .. and 8*7 = 56 ... we did this correctly.
The dimensions of the rectangular room are 8 feet by 7 feet