SOLUTION: A garden has the shape of a right triangle with one leg 9 meters longer than the other. The hypotenuse is 9 meters less than twice the length of the shorter leg. What is the length
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Question 766976: A garden has the shape of a right triangle with one leg 9 meters longer than the other. The hypotenuse is 9 meters less than twice the length of the shorter leg. What is the length of the shorter leg?
PLEEEASE Help! Answer by algebrahouse.com(1659) (Show Source):
You can put this solution on YOUR website! x = one leg
x - 9 = other leg {one leg is 9 shorter than the other}
2(x - 9) - 9 = hypotenuse {the hypotenuse is 9 less than twice the length of the shorter leg}
a² + b² = c² {the Pythagorean Theorem}
a and b are the legs and c is the hypotenuse
x² + (x - 9)² = [2(x - 9) - 9]² {substituted into the Pythagorean Theorem}
x² + (x - 9)² = [(2x - 18) - 9]² {used distributive property}
x² + (x - 9)² = (2x - 27)² {combined like terms in brackets
x² + x² - 18x + 81 = 4x² -108x + 729{used foil method to square the binomials}
2x² - 18x + 81 = 4x² - 108x + 729{combined like terms}
2x² - 90x + 648 = 0 {subtracted 2x² and 81 and added 18x to each side}
x² - 45x + 324 = 0 {divided each side by 2}
(x - 36)(x - 9) = 0 {factored into two binomials}
x - 36 = 0 or x - 9 = 0 {set each factor equal to 0}
x = 36 or x = 9 {solved each equation for x}
x = 36 is the only solution that will work
