SOLUTION: the flower garden has the shape of a right triangle. 5 ft of a perrineal border forms the hypotenuse of the triangle and one leg is 1 ft longer than the other legs, find the length

Algebra ->  Triangles -> SOLUTION: the flower garden has the shape of a right triangle. 5 ft of a perrineal border forms the hypotenuse of the triangle and one leg is 1 ft longer than the other legs, find the length      Log On


   

Question 333575: the flower garden has the shape of a right triangle. 5 ft of a perrineal border forms the hypotenuse of the triangle and one leg is 1 ft longer than the other legs, find the lengths of the legs
Can you please help me thank you
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
When you are dealing with a right triangle and you are trying to find lenght of the sides, you will most likely end up using the pythagorean theorem which states: c%5E2=a%5E2%2Bb%5E2 where c is the side opposite the right angle, and is called the hypotenuse.
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Given in your problem: c=5, a=x and b=x+1
so by the pythagorean theorem of a right triangle: 5%5E2+=+x%5E2+%2B+%28x%2B1%29%5E2
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25=x%5E2+%2B+%28x%5E2%2B2x%2B1%29 (expanding the squared term)
25=2x%5E2%2B2x%2B1 (combining terms)
0=2x%5E2%2B2x-24 (putting the quadratic equation in standard form}}}
0=x%5E2%2Bx-12 (divide the whole thing by 2, to simplify the equation)
0=(x+4)*(x-3) (factor the expression on the right)
x=-4, x=3, since we are dealing with lengths, the negative value x= -4 is extraneous and can be trown out
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so, one side is a=x=3 and the other is b=x+1=4
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what you have is a special type of right triangle where the sides are in a ratio 3:4:5