SOLUTION: 4. the hypotenuse of a right triangle is 5m long.One leg is 1m longer than the other. Find the lengths of the legs.(SET UP AND SOLVE) I thought I submitted this bt it said did n

Algebra ->  Pythagorean-theorem -> SOLUTION: 4. the hypotenuse of a right triangle is 5m long.One leg is 1m longer than the other. Find the lengths of the legs.(SET UP AND SOLVE) I thought I submitted this bt it said did n      Log On


   

Question 187813: 4. the hypotenuse of a right triangle is 5m long.One leg is 1m longer than the other. Find the lengths of the legs.(SET UP AND SOLVE)
I thought I submitted this bt it said did not enter a textbook or something....Anyway, I am very confused by this problem
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

We basically have this triangle set up:





Remember, the Pythagorean Theorem is a%5E2%2Bb%5E2=c%5E2 where "a" and "b" are the legs of a triangle and "c" is the hypotenuse.


Since the legs are x and x%2B1 this means that a=x and b=x%2B1


Also, since the hypotenuse is 5, this means that c=5.


a%5E2%2Bb%5E2=c%5E2 Start with the Pythagorean theorem.


x%5E2%2B%28x%2B1%29%5E2=5%5E2 Plug in a=x, b=x%2B1, c=5


x%5E2%2B%28x%2B1%29%5E2=25 Square 5 to get 25.


x%5E2%2Bx%5E2%2B2x%2B1=25 FOIL


x%5E2%2Bx%5E2%2B2x%2B1-25=0 Subtract 25 from both sides.


2x%5E2%2B2x-24=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=2, b=2, and c=-24


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%28-24%29+%29%29%2F%282%282%29%29 Plug in a=2, b=2, and c=-24


x+=+%28-2+%2B-+sqrt%28+4-4%282%29%28-24%29+%29%29%2F%282%282%29%29 Square 2 to get 4.


x+=+%28-2+%2B-+sqrt%28+4--192+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-24%29 to get -192


x+=+%28-2+%2B-+sqrt%28+4%2B192+%29%29%2F%282%282%29%29 Rewrite sqrt%284--192%29 as sqrt%284%2B192%29


x+=+%28-2+%2B-+sqrt%28+196+%29%29%2F%282%282%29%29 Add 4 to 192 to get 196


x+=+%28-2+%2B-+sqrt%28+196+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%28-2+%2B-+14%29%2F%284%29 Take the square root of 196 to get 14.


x+=+%28-2+%2B+14%29%2F%284%29 or x+=+%28-2+-+14%29%2F%284%29 Break up the expression.


x+=+%2812%29%2F%284%29 or x+=++%28-16%29%2F%284%29 Combine like terms.


x+=+3 or x+=+-4 Simplify.


So the possible answers are x+=+3 or x+=+-4

However, you CANNOT have a negative length.


So the only answer is x+=+3


This means that the first leg "x" is 3 units long


and the second leg "x+1" is 3+1=4 units long



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Answer:

The legs are 3 and 4 units long.