SOLUTION: Can you help me solve: A rectangle is 6cm long and 5cm wide. When each dimension is increased by x cm, the area is tripled. Find the value of x.
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-> SOLUTION: Can you help me solve: A rectangle is 6cm long and 5cm wide. When each dimension is increased by x cm, the area is tripled. Find the value of x.
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You can put this solution on YOUR website! The Area A of a rectangle is found by multiplying the length L times the width W. In this
problem you are told that the length L is 6 cm and the width W is 5 cm. Therefore,
the Area is L times W and this is 6 times 5 = 30 square cm.
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Next we are going to increase L by x cm, making the new length (6 + x) cm. We are also going
to increase W by the same x cm, making the new width (5 + x) cm. As a result the new
Area will be 3 times the old area or 3 times 30 square cm which is 90 sq cm.
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We can write the equation for the new area resulting from the new length times the new width.
This equation is:
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.
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Multiply out the right side using the FOIL method (multiply Firsts, Outsides, Insides, then
Lasts and add them all together).
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Firsts =
Outsides =
Insides =
Lasts =
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Adding them all together gives . This equals the
new area. Therefore, set it equal to 90. When you do the equation becomes:
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Subtract 90 from both sides to eliminate the 90 on the right side. When you do this subtraction
you get:
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Notice that the left side can be factored. When you do the factoring you get:
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This equation will be true if either of the two factors equals zero because zero times anything
on the left side will make the left side equal the zero on the right side. So set the
two factors equal to zero, one at a time.
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Subtract 15 from both sides to eliminate the 15 on the left side. When you do that you
get . This doesn't make sense. Instead of adding to the original dimensions
we would be taking away from them ... adding a negative 15. So we ignore this solution.
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Next
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Add 4 to both sides to eliminate the -4 on the left side. This results in:
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That's more like what we might expect. Let's try it by adding 4 cm to each of the original
dimensions and see what the new area will be. The original length was 6 cm. If we add 4 cm
to it we get a new length of 10 cm. And the original width was 5 cm. If we add 4 cm to it
we get a new width of 9 cm.
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The new area will be the new length times the new width or cm.
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Everything checks out so your answer is x = +4 cm.
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I hope this helps you to understand the problem better.
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