SOLUTION: A right triangle has one leg twice as long as the other. Find a function that models its perimeter P in terms of the length x of the shorter leg.

Algebra ->  Triangles -> SOLUTION: A right triangle has one leg twice as long as the other. Find a function that models its perimeter P in terms of the length x of the shorter leg.       Log On


   



Question 226277: A right triangle has one leg twice as long as the other. Find a function that models its perimeter P in terms of the length x of the shorter leg.

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
A right triangle has one leg twice as long as the other. Find a function that models its perimeter P in terms of the length x of the shorter leg.

Step 1. The perimeter P means adding up all the three sides of a triangle.

Step 2. Let x be the shorter leg.

Step 3. Let 2x be the longer leg.

Step 4. Use Pythagorean Theorem which states that the squares of the legs of a right triangle (given as x and 2x) is equal to the square of the hypotenuse c.

c%5E2=x%5E2%2B%282x%29%5E2

c%5E2=5x%5E2

Take the square root to both sides of the equation

c=x%2Asqrt%285%29

Step 5. Then, P=x%2B2x%2Bx%2Asqrt%285%29=x%283%2Bsqrt%285%29%29.

Step 6. ANSWER: The Perimeter P=x%283%2Bsqrt%285%29%29

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

drjctu@gmail.com

http://www.FreedomUniversity.TV
http://www.Facebook.com/FreedomUniversity.TV
http://www.Twitter.com/FreedomUTV