SOLUTION: A room has an area of 418 square feet. One dimension is 3 feet more than the other. Find the dimensions of the room.

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Question 464109: A room has an area of 418 square feet. One dimension is 3 feet more than the other. Find the dimensions of the room.


Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

A room has an area of A=418ft%5E2.
One dimension (length=L) is 3 feet more than the other (width=W.
L=W%2B3ft

Find the dimensions of the room.

A=418ft%5E2

L%2AW=418ft%5E2......substitute L

%28W%2B3ft%29%2AW=418ft%5E2

W%5E2%2B3Wft=418ft%5E2

W%5E2%2B3Wft-418ft%5E2=0..use quadratic formula

W=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

W=+%28-3ft+%2B-+sqrt%28+%283ft%29%5E2-4%2A1%2A%28418ft%5E2%29+%29%29%2F%282%2A1%29+

W=+%28-3ft+%2B-+sqrt%28+9ft%5E2%2B1672ft%5E2+%29%29%2F2+
W=+%28-3ft+%2B-+sqrt%28+1681ft%5E2+%29%29%2F2+
W=+%28-3ft+%2B-+41ft+%29%2F2+
we need only positive root because width cannot be negative
W=+%28-3ft+%2B+41ft+%29%2F2+

W=+%2838ft+%29%2F2+

W=+19ft+
now find the length
L=W%2B3ft
L=19ft%2B3ft
L=22ft