Answer:
y = 3[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
y² = x² + x² = 3² + 3² = 9 + 9 = 18 ( take the square root of both sides )
y = [tex]\sqrt{18}[/tex] = [tex]\sqrt{9(2)}[/tex] = [tex]\sqrt{9}[/tex] × [tex]\sqrt{2}[/tex] = 3[tex]\sqrt{2}[/tex]
Applying the Pythagorean Theorem, it is found that the value is [tex]y = 3\sqrt{2}[/tex].
The Pythagorean Theorem states that in a right triangle, which has an angle of 90º, the sum of the lengths squared of the sides is equals to the length squared of the hypotenuse.
In this problem:
Hence, applying the Theorem:
[tex]x^2 + x^2 = y^2[/tex]
[tex]y^2 = 2x^2[/tex]
Since [tex]x = 3[/tex]:
[tex]y^2 = 2(3)^2[/tex]
[tex]y = \sqrt{2 \times 3^2}[/tex]
[tex]y = 3\sqrt{2}[/tex]
A similar problem involving the Pythagorean Theorem is given at https://brainly.com/question/21691542
