Question

I need help on this???

Answer 1

Use the geometric mean for right triangles here.  Like this $\frac{9}{y}= \frac{y}{7}$.  Cross multiply to get $y^{2}=63$, and $y= \sqrt{63}$.  That simplifies down to $y= \sqrt{9*7}$.  Pull out the 9 as a perfect square of 3 and you're left with $y=3 \sqrt{7}$, first choice above.

Answer 2

Another way to do this is to apply pythagoras 3 times, since there are 3 right triangles. Assuming the sides not named here are a and b, you get:

a^2 + b^2 = 16^2
9^2 + y^2 = a^2
y^2 + 7^2 = b^2

You can solve these to y=3√7