SOLUTION: A rectangular room containing 154 square feet is 3 feet longer than it is wide. How long of a piece of crown molding is needed to trim the perimeter of the ceiling?
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Question 1128377: A rectangular room containing 154 square feet is 3 feet longer than it is wide. How long of a piece of crown molding is needed to trim the perimeter of the ceiling? Found 2 solutions by ikleyn, addingup:Answer by ikleyn(52781) (Show Source):
154 = 11*14 is the decomposition of the number 154 into the product of two factors that differ by 3: 14 - 11 = 3.
Therefore, the dimensions of the room are 11 by 14 feet.
Alternatively, you can find these dimensions by solving quadratic equation
x*(x+3) = 154.
Having dimensions, you can easily find the perimeter.
Answer. 11 + 14 + 11 + 14 = 50 feet.
You can put this solution on YOUR website! length: l
width: w
l = w + 3
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l * w = 154
substitute for l:
(w + 3)w = 154
rewrite like this:
w(w + 3) = 154
distribute the first w, multiply times the terms inside the parenthesis like this:
w^2 + 3w = 154
w^2 + 3w - 154 = 0
Let's try to factor this equation. Find two factors of -154 that add up to the coefficient of the middle term which is 3 (I already did it, you can do it on your own - Note: factoring is very important in math, practice it):
(w+ 14)(w -11) = 0
w + 14 = 0 or w - 11 = 0
w = -14 or w = 11
we are not looking for a negative number, so let's try 11:
(11 + 3)11 = 154
121 + 33 = 154
154 = 154 Correct
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So, we have that the width of the room is 11 feet and the length is 14 feet. And the room has 4 walls: 2(11) + 2(14) = 50 you need 50 feet of crown molding.
