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. 


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^2=x^2+(2x)^2}}}


{{{c^2=5x^2}}}


Take the square root to both sides of the equation


{{{c=x*sqrt(5)}}}


Step 5.  Then, {{{P=x+2x+x*sqrt(5)=x(3+sqrt(5))}}}.


Step 6.  ANSWER:  The Perimeter {{{P=x(3+sqrt(5))}}}


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


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