Analyze the diagram below and complete the instructions that follow. Find the value of x

One of the rules of triangles is that if you have a 45 45 90 angle triangle, the two sides besides the hypotenuse are equal to each other. In this case, one of the sides is equal to x, so other side is equal to x as well. Now, to solve for x, you need to know the Pythagorean theorum:

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

Both 'a' and 'b' are equal to x, and 'c' is equal to 3, so I'll make the substitutions below:

[tex] {x}^{2} + {x}^{2} = {3}^{2} [/tex]

This can be simplified to:

[tex] {2x}^{2} = 9[/tex]

Now we just solve for x:

[tex] \frac{2}{2} {x}^{2} = \frac{9}{2} [/tex]

[tex] \sqrt{ {x}^{2} } = \sqrt{ \frac{9}{2} } [/tex]

[tex] x = \frac {\sqrt {9}}{\sqrt {2}} \times \frac {\sqrt {2}}{\sqrt {2}} [/tex]

Solution:

[tex] \frac {3\sqrt {2}}{2} [/tex]