SOLUTION: Will someone show me the steps to solve this problems so that I will be able to work othere like this or similar to it. The shorter leg of a right triangle is 11 meters. The hyp

Algebra ->  Formulas -> SOLUTION: Will someone show me the steps to solve this problems so that I will be able to work othere like this or similar to it. The shorter leg of a right triangle is 11 meters. The hyp      Log On


   

Question 76799: Will someone show me the steps to solve this problems so that I will be able to work othere like this or similar to it.
The shorter leg of a right triangle is 11 meters. The hypotenuse is 1 meter longer than the longer leg. Find the length of the longer leg.
Thank you,
Sabrina
Found 2 solutions by Earlsdon, funmath:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Since the problem is about a right triangle, think about using the Pythagorean theorem: c%5E2+=+a%5E2+%2B+b%5E2 Where: c is the length of the hypotenuse and a & b are the lengths of the two legs.
In this problem, you are given the length of one of the legs (11 m.) and you are told that the length of the hypotenuse is 1 meter longer than the other (longer) leg.
So, we'll let x meters be the length of the longer leg.
Then the length of the hypotenuse will be x+1 meters.
Now let's apply the Pythagorean theorem.
%28x%2B1%29%5E2+=+11%5E2+%2B+x%5E2 Simplify this.
x%5E2%2B2x%2B1+=+121+%2B+x%5E2 Subtract x%5E2 from both sides of the equation.
2x%2B1+=+121 Now subtract 1 from both sides.
2x+=+120 Finally, divide both sides by 2.
x+=+60
The length of the longer leg is 60 meters.

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Hi Sabrina,
The Pythagorean Theorem says that the hypotenuse squared is equal to the sum of the squares of the legs.
c%5E2=a%5E2%2Bb%5E2
The shorter leg of a right triangle is 11 meters. The hypotenuse is 1 meter longer than the longer leg. Find the length of the longer leg.
let the shorter leg be a=11
let the longer leg be b=x
then the hypotenuse is: x+1
Plug them into the Pythagorean Theorem and you get:
%28x%2B1%29%5E2=%2811%29%5E2%2B%28x%29%5E2
%28x%2B1%29%28x%2B1%29=121%2Bx%5E2
x%5E2%2Bx%2Bx%2B1=121%2Bx%5E2
x%5E2%2B2x%2B1=121%2Bx%5E2
x%5E2-x%5E2%2B2x%2B1=121%2Bx%5E2-x%5E2
2x%2B1=121
2x%2B1-1=121-1
2x=120
2x%2F2=120%2F2
x=60
The Longer leg is b=x=60 m
(The hypotenuse would be 60+1=61 m they didn't ask for that, but they could have.)
Happy Calculating!!!!