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Find the PERIMETER of this triangle

Find the PERIMETER of this triangle-example-1

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Answer: The perimeter of the triangle given is: " 24 units " .
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Step-by-step 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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User Johnny Pauling
by
7.2k points
2 votes
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 = √(100 - 36)
Subtract,


a = √(64)
Solve for the root,


a = 8
~~

So our missing length is 8.

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

~~


8 + 10 + 6 = 24

~~

Answer : 24

~~

I hope that helps you out!!

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

~Zoey
User Yalewzj
by
8.1k points

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