Triangles QST and RST are similar. Therefore, the following is true:
q s
--- = ---- This results in 10q=rs.
r 10
Also, since RST is a right triangle, 4^2 + s^2 = q^2.
Since QST is also a right triangle, s^2 + 10^2 = r^2.
4 s
Also: ---- = ----- which leads to s^2 = 40
s 10
Because of this, 4^2 + s^2 = q^2 becomes 16 + 40 = 56 = q^2
Then q = sqrt(56) = sqrt(4)*sqrt(14) = 2*sqrt(14) (answer)
The opposite angles equal each other, so X and Z are equal
using that we solve for x by setting them equal:
6x-60 = 2x+68
subtract 2x from each side:
4x -60 = 68
add 60 to each side:
4x = 128
divide both sides by 4
x = 128/4
x = 32
now we know x so we can solve everything else by replacing x with 32
WY = 3x+5 = 3(32)+5 = 96+5 = 101
angle Z = 2x+68 = 2(32)+68 = 64+132
the answer is C
