SOLUTION: I just don't get word problems! the two sides of a right triangle differ by one. If the hypotenuse is 29cm, then determine the lengths of the two sides. How do I solve using the qu

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Question 324504: I just don't get word problems! the two sides of a right triangle differ by one. If the hypotenuse is 29cm, then determine the lengths of the two sides. How do I solve using the quadratric formula.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"the two sides of a right triangle differ by one" means that the two legs of the triangle are 'x' and 'x+1'


Since "the hypotenuse is 29cm", we know that by the pythagorean theorem, we get the equation x%5E2%2B%28x%2B1%29%5E2=29%5E2


x%5E2%2B%28x%2B1%29%5E2=29%5E2 Start with the given equation.


x%5E2%2B%28x%2B1%29%5E2=841 Square 29 to get 841


x%5E2%2Bx%5E2%2B2x%2B1=841 FOIL


x%5E2%2Bx%5E2%2B2x%2B1=841 FOIL


x%5E2%2Bx%5E2%2B2x%2B1-841=0 Subtract 841 from both sides.


2x%5E2%2B2x-840=0 Combine like terms.


Notice that the quadratic 2x%5E2%2B2x-840 is in the form of Ax%5E2%2BBx%2BC where A=2, B=2, and C=-840


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%282%29+%2B-+sqrt%28+%282%29%5E2-4%282%29%28-840%29+%29%29%2F%282%282%29%29 Plug in A=2, B=2, and C=-840


x+=+%28-2+%2B-+sqrt%28+4-4%282%29%28-840%29+%29%29%2F%282%282%29%29 Square 2 to get 4.


x+=+%28-2+%2B-+sqrt%28+4--6720+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-840%29 to get -6720


x+=+%28-2+%2B-+sqrt%28+4%2B6720+%29%29%2F%282%282%29%29 Rewrite sqrt%284--6720%29 as sqrt%284%2B6720%29


x+=+%28-2+%2B-+sqrt%28+6724+%29%29%2F%282%282%29%29 Add 4 to 6720 to get 6724


x+=+%28-2+%2B-+sqrt%28+6724+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%28-2+%2B-+82%29%2F%284%29 Take the square root of 6724 to get 82.


x+=+%28-2+%2B+82%29%2F%284%29 or x+=+%28-2+-+82%29%2F%284%29 Break up the expression.


x+=+%2880%29%2F%284%29 or x+=++%28-84%29%2F%284%29 Combine like terms.


x+=+20 or x+=+-21 Simplify.


So the possible solutions are x+=+20 or x+=+-21

Since a negative length doesn't make sense, this means that we're going to ignore x+=+-21


So this means that one leg is x=20 cm long. So the next leg is x%2B1=20%2B1=21 cm long.


So the lengths of the two legs are 20 cm and 21 cm.