Question 419199: 6. In the two squares shown below, the longer square has a side length 1 foot greater than that of the
smaller square. If the combined area of the two squares is 113 square feet, find the length of the
side of the smaller square. (Define any variables that you use by using let statements and/or by
labeling the diagram.)
Answer by duckness73(47)   (Show Source):
You can put this solution on YOUR website! Let x = length of the side of the small square. This means that:
x + 1 = length of the side of the large square.
The area of the small square is x^2
The area of the large square is (x + 1) ^ 2
Since the combined area of the two squares is 113, we have
x^2 + ((x + 1) ^ 2) = 113
x^2 + (x^2 + 2x + 1) = 113 (expanding the expression)
2x^2 + 2x + 1 = 113 (combining like terms)
2x^2 + 2x - 112 = 0 (subtracting 113 from both sides)
x^2 + x - 56 = 0 (dividing both sides by 2)
(x - 7)(x + 8) = 0 (factoring)
x = 7 or x = -8 (setting each factor to zero and solving)
So, the side of the small square is either 7 or -8. Since it doesn't make sense for a square to have a side -8 units long, the side of the small square is 7.
Answer: the length of the side of the small square is 7. (And, BTW, the length of the side of the large square is x + 1 = 7 + 1 = 8).
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