Respuesta :

semsee45

Answer:

Perimeter = 30 in

Step-by-step explanation:

Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

  • a = a
  • b = 12 in
  • c = 13 in

Substitute given values into the formula and solving for a:

⇒ a² + 12² = 13²

⇒ a² + 144 = 169

⇒ a² = 25

⇒ a = 5 in

Therefore, perimeter = a + b + c

                                   = 5 in + 12 in + 13 in

                                   = 30 in

Ankit

Final Answer:

[tex]\fbox{perimeter \: of \: triangle = 30 \: in.}[/tex]

Step by Step explanation:

Data achieved from diagram:

The given triangle is a right angle triangle

Hypotenuse of triangle = 13 in.

Base of triangle = 12 in.

To find:

Perimeter of triangle = ?

Solution:

We need length of all three sides (Altitude) of triangle,

let's find out the measure of length of Altitude using Pythagoras theorem!

[tex]{Hypotenuse}^2 = {Base}^2 + {Altitude}^2 \\ {13}^{2} = {12}^{2} + {A}^{2} \\ {A}^{2} = 169 - 144 \\ {A}^{2} = 25 \\ {A} = \sqrt{25 } \\ \fbox{A = 5 \: in.}[/tex]

Now we have all three sides of triangle,

[tex]perimeter \: of \: triangle = Hyp. + Base + Alt. \\perimeter \: of \: triangle = 13 + 12 + 5 \\ \fbox{perimeter \: of \: triangle = 30 \: in.}[/tex]

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