Question

Find the value of x.

A:
2 square root of 6

B:
2 square root of 42

C:
2 square root of 7

D:
square root of 14

Answer 1

If we call the leg of the small triangle y, and the leg perpendicular to x z, we can apply Pythagoras 3 times:

(1) 4 + y^2 = x^2
(2) x^2 + z^2 = 196 => z^2 = 196-x^2
(3) y^2 + 144 = z^2 => y^2 = z^2 - 144

Now fill in (3) in (1):

4 + z^2 - 144 = x^2

and then (2) in (1):

196-x^2-140 = x^2 => 2x^2 = 56 => x = √28 = 2√7

Answer C!