Question 102860: PLEASE HELP ME WITH THIS!!
IF THE LENGTH OF THE SIDE OF A SQUARE IS INCREASED BY 6 UNITS, THE AREA IS MULTIPLIED BY 4. FIND THE ORIGINAL LENGTH.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! If you call the side of the original square x, then the area of the original square is x^2.
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Now increase the length of each side by 6 units. So each side of the new square is x + 6.
This means that the area of this new square Bis (x + 6)^2 which multiplies out to x^2 + 12x + 36.
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But the area new square is 4 times the area of the old square ... or 4x^2. So set the area
of the new square equal to 4 times the area of the old square. In equation form this is
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x^2 + 12x + 36 = 4x^2
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To put this into a more standard form, subtract 4x^2 from both sides to get:
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-3x^2 + 12x + 36 = 0
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Note that -3 is a factor of all terms on the left side. Therefore you can simplify
this equation by dividing both sides (all terms) by -3 to reduce the equation to:
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x^2 - 4x - 12 = 0
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Factor the left side to get:
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(x - 6)(x + 2) = 0
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Notice this equation is true if either of the two factors on the left side equals zero.
So set each factor equal to zero and solve for x.
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x - 6 = 0 ... add 6 to both sides to get x = 6. This is one possible answer.
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x + 2 = 0 ... subtract 2 from both sides to get x = -2 ... another possible answer.
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But having a side of square equal to -2 doesn't make any sense. So the only reasonable answer
is that x ... the side of the original square ... is 6.
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Let's check the answer. If the sides of the original square are 6 units, then the area of
the original square is 6 times 6 or 36 square units.
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Increasing each side of the original square by 6 units makes the new square have sides of
12 units. Therefore, the area of the new square is 12 times 12 or 144 square units.
Notice that the area of the new square is 4 times the area of the original square ...
4 times 36 equals 144 square units.
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Hope this helps you to understand the problem.
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