Respuesta :

Mickeym175

Answer:

4

Step-by-step explanation:

We use the Pythagorean theorem [tex]a^2+b^2=c^2[/tex]

a and b are the shortest sides (legs)

C is the longest side (hypotenuse)

So we fill in what we know into the formula to find the missing side

[tex]\sqrt{65}^2+b^2=9^2[/tex]

Simplify

[tex]65+b^2=81[/tex]

Subtract both sides by 65

[tex]b^2=16[/tex]

Square root both sides

[tex]b=4[/tex]

The missing side is equal to 4

Answer:

third side = 4

Step-by-step explanation:

using Pythagoras' identity in the right triangle

a² + b² = c²

c is the hypotenuse and a, b the two sides

let x be the third side, then

a = x, b = [tex]\sqrt{65}[/tex] , c = 9

substitute these values into the identity

x² + ( [tex]\sqrt{65}[/tex] )² = 9²

x² + 65 = 81 ( subtract 65 from both sides )

x² = 16 ( take square root of both sides )

[tex]\sqrt{x^2}[/tex] = [tex]\sqrt{16}[/tex], that is

x = 4

The third side is 4

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