SOLUTION: the hypotenuse of a right triangle is 26 feet long.one leg is fourteen feet longer than the other.find the lentgh of the shorter leg?

Question 265516: the hypotenuse of a right triangle is 26 feet long.one leg is fourteen feet longer than the other.find the lentgh of the shorter leg?
Answer by roseo(33) (Show Source): You can put this solution on YOUR website!
Let one side of the triangle be x and then the other leg of the triangle will be x+14. By using the Pythagorean Theorem we would have
x^2+(x+14)^2=26^2
x^2 +x^2+28x+196 = 676
By combining like terms and putting everything on one side we have
2x^2+28x-480=0
To simplify divide both sides by 2
x^2+14x-240=0
By factoring we have
(x+24)(x-10)=0
So the x+24=0 and x-10=0, therefore
x=-24 and x=10,
x=-24 is a nonsense answer be the side of a triangle cannot have a negative measure so one leg of the triangle is 10 and the other would be x+14 or 24.
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