Question 171507: Given the triange with a hypotenuse = 20 , and one leg = X + 8 , and the other leg = X
Approximate to the nearest foot how many feet of walking distance a person saves by cutting across the lawn instead of walking on the side walk.
I know you use pythagorean theorem to get {2x^2 + 16x -336 = 0}
then simplify and get 2(x^2 + 8x - 168) = 0
After this you use quadratic equation and get -4 +- ^736 over 1
I dont know how to get the whole number after this
Thanks
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Given the triange with a hypotenuse = 20 , and one leg = X + 8 , and the other leg = X
Approximate to the nearest foot how many feet of walking distance a person saves by cutting across the lawn instead of walking on the side walk.
I know you use pythagorean theorem to get {2x^2 + 16x -336 = 0}
then simplify and get 2(x^2 + 8x - 168) = 0
After this you use quadratic equation and get -4 +- ^736 over 1
I dont know how to get the whole number after this
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You get -4 + sqrt(184) and
-4 - sqrt(184). It's sqrt(736)/2
Since it's a length, ignore the negative answer and use
-4 + sqrt(184) = ~ 9.564 feet
or 10' to the nearest foot.
The 2 legs are 10 and 18. That's 8' more than the hypotenuse.
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website! You were headed down the right path but made one little mis-step.
Your equation is correct: 
Your evaluation of the quadratic formula was correct up to a point, so let's review:
 So far, so good.
But then you simplified to  which is incorrect because you only divided ONE of the numerator terms by the denominator. That is against the rules: the other team gets a penalty kick.
What you need to do is find the prime factorization of 736.
736/2 = 368
368/2 = 184
184/2 = 92
92/2 = 46
46/2 = 23
23 is prime
Now you can say  and 
Going back to where you were before you went astray:
 is negative, so exclude this root as extraneous.
Evaluate  which gets you approximately 9.56, the length of the short leg of the triangle. Since the longer leg is 8 feet longer, the longer leg must be approximately 17.56 feet. If you walk the sidewalk, you have to go 17.56 feet plus 9.56 feet or 27.12 feet. If you walk the diagonal, you only have to walk 20 feet. The difference is 27.12 - 20 = 7.12. Rounded to the nearest foot, 7 feet.
Notice that I didn't do the round-off until the very last step. Whenever you round numbers, you introduce errors, so it is important to keep greater precision (typically 1 or 2 decimal places greater precision than the precision required in the answer) until you have made your final calculation.
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