SOLUTION: A right triangle has one leg three times 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 three times 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 217797: A right triangle has one leg three times 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 three times 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. Let x be the shorter leg.

Step 2. Let 3x be the longer leg and since it is three times longer than the shorter leg.

Step 3. Perimeter P means we add up all three sides of a triangle.

Step 4. Use Pythagorean Theorem to find the hypotenuse which states that the sum of the squares of the legs (x and 3x) is equal to the sum of the squares of the hypotenuse.

c%5E2=x%5E2%2B%283x%29%5E2=x%5E2%2B9x%5E2=10x%5E2 where c is the hypotenuse

c=x%2Asqrt%2810%29

Step 5. So P=x%2B3x%2Bx%2Asqrt%2810%29=4x%2Bx%2Asqrt%2810%29=x%281%2Bsqrt%2810%29%29

Step 6. ANSWER is P=x%2A%281%2Bsqrt%2810%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