Find the PERIMETER of this triangle

First we need to find the missing side, use

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

Let's substitute the numbers,

[tex]a = \sqrt{ {10}^{2} - {6}^{2} } [/tex]
Solve for the squares,

[tex]a = \sqrt{100 - 36} [/tex]
Subtract,

[tex]a = \sqrt{64} [/tex]
Solve for the root,

[tex]a = 8[/tex]
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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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[tex]8 + 10 + 6 = 24[/tex]

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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

JonHenderson55 JonHenderson55 · Answer 2 · 2018-03-22T14:44:26+01:00

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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