Question

What is the value of a?

Answer 1

Actually, the answer is not A, if you're saying A is the first choice above.  That's incorrect.  You will need to use the Geometric mean for right triangles here to figure out what the value of a is.  We will use this form: $\frac{YZ}{WZ} = \frac{WZ}{XZ}$.  We have a value for YZ of 3; side a is XZ.  That means in order to solve this we need WZ, which we can find using pythagorean's theorem.  3^2 + 4^2 = c^2 and 9 + 16 = c^2 and c = 5.  Now we fill in accordingly: $\frac{3}{5}= \frac{5}{XZ}$.  Cross-multiply to get 3XZ=25 and side XZ is $\frac{25}{3}$.  XZ is 25/3 and YZ is 3, so 25/3 - 3 = XY.  That means that XY (side a) = 16/3 or 5 1/3, choice B, or the second one down.