Find the perimeter of this triangle

 The perimeter of the triangle given is:  " 24 units " . 

Explanation:

        To find the perimeter of the triangle, we add up the lengths of
  all 3 (THREE) sides of the triangle; and we have the answer!

The triangle given is a "right triangle.

We are given the length of 2 (TWO) of the sides:  "6 units" ; and "10 units (the length of the hypotenuse). 

We can find the "unknown side length" by using the "Pythagorean theorem" (since this is a "right trangle"):

       →   a²  +  b²  = c²  ;  

                          in which : "c" is the hypotenuse; which is:  "10" (given); 

Let "b" represent the known side length, which is "6" (given). 

Solve for "a" (the "unknown" side length).

         →  a²  +  6²  =  10²  ;   Solve for "a" ;

         →  a²  =  10²  –  6²  = 100 – 36 = 64 .

         ↔  a² = 64 . 

Now, take the positive square root of each side of the equation; 
      to isolate "a" on one side of the equation; & to solve for "a" ; 

         →   ⁺√(a²) = √64 ; 

         → a = 8 .

Now, to find the "perimeter" of the triangle, we add up all of the side lengths:

   6 + 8 + 10 =  14 + 10 = 24 . 

 The perimeter of the triangle given is:  " 24 units " . 

The point (5, 10) will work for the rule y=x+5.y= 10 x= 510=5+510=10therefore the ordered pair (5, 10) works for the rule