Question 115240: I need help with this one.
A room has an area of 300 square fee. One dimension is 5 feet more than the other. Find the dimensions of the room.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Assume the room is rectangular in shape.
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The area (A) of the rectangular room is the product of its length (call it L) times its
width (call it W). In equation form this is:
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A = L*W
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The problem tells you that the area is 300 square feet. Substitute this value for A in the
equation to get:
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300 = L*W
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Next the problem tells you that one dimension is 5 feet longer than the other. Since the
length is normally defined as being the longer of the two dimensions, we can say that the
length is 5 feet longer than the width. That means the length will equal the width if
you add 5 feet to the width. In equation form this is:
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L = W + 5
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You can substitute W + 5 for L in the area equation because W + 5 is equal to L. When you
make that substitution you get:
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300 = (W + 5)*W
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Multiply out the right side and the equation becomes:
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300 = W^2 + 5W
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Get rid of the 300 on the left side by subtracting 300 from both sides and the equation is
transformed to:
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0 = W^2 + 5W - 300
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Get this into a more familiar form by transposing this equation (switching sides) and
you have:
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W^2 + 5W - 300 = 0
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Factor the left side:
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(W + 20)(W - 15) = 0
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This equation will be true if either of the two factors is zero, because then the left
side will involve a multiplication by zero and will, therefore, equal the zero on the
right side. So set each of the factors equal to zero and solve for W.
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W + 20 = 0
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Subtract 20 from both sides to get rid of the 20 on the left side and you get:
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W = -20
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Ignore this answer because it makes no sense to have a negative dimension for a room.
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Next set the other factor equal to zero:
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W - 15 = 0
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Get rid of the -15 on the left side by adding 15 to both sides of the equation and you
have:
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W = 15
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So W, the width, equals 15 feet. And the length is 5 feet more than the width. Therefore, the
length is 15 plus 5 or 20 feet.
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The dimensions of the room are 15 feet by 20 feet.
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And if you multiply these dimensions together you will see that the product is 300 square
feet. Our answer checks.
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Hope this helps you to understand the problem and how to work it.
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