Question

Find x
Pleasee! Help! Soon!

Answer 1

Answer:
`x = (7√(6))/(2)\\\\`

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Step-by-step explanation:

Focus on the upper triangle. This is a 30-60-90 triangle. The short leg is 7 and the long leg is
`7√(3)`. The long leg is always sqrt(3) times that of the short leg (and this only works for 30-60-90 triangles).

In short, the horizontal length is
`7√(3)` units long.

Now move to the lower triangle. This is a 45-45-90 triangle with congruent legs (each are x units long). We just found the hypotenuse is
`7√(3)`

We can use the pythagorean theorem to say the following:

`a^2 + b^2 = c^2\\\\x^2 + x^2 = (7*√(3))^2\\\\2x^2 = 147\\\\x^2 = (147)/(2)\\\\x = \sqrt{(147)/(2)}\\\\x = (√(147))/(√(2))\\\\x = (√(147)*√(2))/(√(2)*√(2))\\\\x = (√(147)*√(2))/(2)\\\\x = (√(147*2))/(2)\\\\x = (√(294))/(2)\\\\x = (√(49*6))/(2)\\\\x = (√(49)*√(6))/(2)\\\\x = (7√(6))/(2)\\\\`