Respuesta :

Answer :

  • 6.40. (Option 3)

[tex] \\ [/tex]

Step-by-step explanation :

Here, A right angled triangle is given with the measure of two sides and we are to find the measure of the third side.

We'll find the measure of third side with the help of the Pythagorean theorem,

[tex]\\ {\longrightarrow \pmb{\sf {\qquad (Hypotenuse {)}^{2}= (Base) {}^{2} + (Perpendicular {)}^{2} }}} \\ \\[/tex]

Here,

  • The base (BC) is 4

  • The perpendicular (AC) is 5

  • The hypotenuse (AB) is c.

[tex] \\ [/tex]

So, substituting the values in the formula we get :

[tex]\\ {\longrightarrow \pmb{\sf {\qquad (c {)}^{2}= (4) {}^{2} + (5 {)}^{2} }}} \\ \\[/tex]

[tex] {\longrightarrow \pmb{\sf {\qquad (c {)}^{2}= 16 + 25 }}} \\ \\[/tex]

[tex] {\longrightarrow \pmb{\sf {\qquad (c {)}^{2}= 41 }}} \\ \\[/tex]

[tex] {\longrightarrow \pmb{\sf {\qquad c = \sqrt{41} }}} \\ \\[/tex]

[tex] {\longrightarrow \pmb{\frak {\qquad c \approx 6.40 }}} \\ \\[/tex]

Therefore,

  • The measure of the third side (c) is 6.40 .
SupremeStrange

Step-by-step explanation:

As it is a right angle triangle , So

  • Hypotenuse = C units
  • Base = 4 units
  • perpendicular = 5 units

We have to find the value of hypotenuse i.e C

By Pythagoras theorem

H² = P² + B²

putting the known values ,

C² = 5² + 4²

C² = 41 units

C = √41 units

C = 6.40 units

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