Question

What is the value of x to the nearest tenth?

Answer 1

x is the radius of the circle.  If we draw another radius to the end of the chord, we get a right triangle with legs 12 (half of 24) and 6, and hypotenuse x.  We write the Pythagorean Theorem

$x^2 = 12^2 + 6^2 = 144 + 36 = 180$

$x = \sqrt{180} = \sqrt{36 \times 5} = 6 \sqrt{5}$

I don't like the calculator part; why ruin a nice exact answer with an approximation?  But for completeness

$x \approx 13.4$