Question 612626
    one leg of a right triangle measures three inches less than the other leg. find the length of both legs if the hypotenuse is 4 inches long
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Let x = longer leg
then
x-3 = shorter leg
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applying Pythagorean theorem:
x^2 + (x-3)^2 = 4^2
x^2 + (x-3)(x-3) = 16
x^2 + x^2-6x+9 = 16
2x^2-6x+9 = 16
2x^2-6x-7 = 0
applying the "quadratic formula" yields:
x = {3.9, -0.9}
throw out the negative solution (extraneous) leaving
x = 3.9 inches (longer leg)
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shorter leg:
x-3 = 3.9-3 = .9 inches
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answer: 3.9 inches and .9 inches
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details of quadratic formula follows:
*[invoke quadratic "x", 2, -6, -7 ]