Question

Find the PERIMETER of this triangle

Answer 1

First we need to find the missing side, use

$a = \sqrt{ {c}^{2} - {b}^{2} }$
So the missing leg = the sqrt of the hypotenuse squared minus the other leg squared.

Let's substitute the numbers,

$a = \sqrt{ {10}^{2} - {6}^{2} }$
Solve for the squares,

$a = \sqrt{100 - 36}$
Subtract,

$a = \sqrt{64}$
Solve for the root,

$a = 8$
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So our missing length is 8.

To find the perimeter of the triangle, simply add all the sides....

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$8 + 10 + 6 = 24$

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Answer : 24

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I hope that helps you out!!

Any more questions, please feel free to ask me and I will gladly help you out!!

~Zoey

Answer 2

Answer:  The perimeter of the triangle given is:  " 24 units " . 
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Explanation:
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        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!
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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). 
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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 .
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Now, to find the "perimeter" of the triangle, we add up all of the side lengths:

   6 + 8 + 10 =  14 + 10 = 24 . 
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Answer:  The perimeter of the triangle given is:  " 24 units " . 
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