Respuesta :
We will calculate the length of the hypotenuse using the Pythagorean theorem. Suppose that the hypotenuse = c, then:
c^2 = 6^2 + 3^2
c^2 = 36 + 9
c^2 = 45
c = square root of 45
c = square root of 9 * square root of 5
c = 3 * square root of 5 ; square root of 5 = approximately 2,24
c = 3 * 2,24 = 6,72 = 6,7
The correct answer is 6,7.
Pythagoras theorem states that, in a right angle triangle the square of the length of the hypotenuse is equal to the sum of the square of the other two sides.The length of the hypotenuse for the given right angle triangle to the nearest tenth is 6.7 cm. Thus the option 2 is the correct option.
Given information.
The length of the one leg of the right angle triangle is 6 cm.
The length of the another leg of the right angle triangle is 3 cm.
Pythagoras theorem-
According to the Pythagoras theorem, in a right angle triangle the square of the length of the hypotenuse is equal to the sum of the square of the other two sides.
Suppose the length of the hypotenuse for the given right angle triangle is x cm. Thus,
[tex]x^2=6^2+3^2[/tex]
[tex]x^2=36+9[/tex]
[tex]x=\sqrt{45} [/tex]
[tex]x=6.7082[/tex]
Thus the length of the hypotenuse for the given right angle triangle is 6.7082 cm.
The length of the hypotenuse for the given right angle triangle to the nearest tenth is 6.7 cm. Thus the option 2 is the correct option.
Learn more about the Pythagoras theorem here;
https://brainly.com/question/343682
