Question

What is x?

A.2√5
B.3√5
C.6

Answer 1

use pythagorean theorem on larger triangle to get x

Answer 2

using x value solve for y from smaller rt angled triangle using pythagorean theorem again!

Answer 3

That drawing is obviously not made to scale, judging from the segments labeled 4 and 5 :-)

You've got two similar triangles. 4:x as x:9 because the corresponding sides must be proportional. From that you can find the value of x.

Answer 4

:)

Answer 5

@AravindG my first instinct was to go the way you suggested, but without a known relationship between x and y, I ran into a roadblock.

Answer 6

i see

Answer 7

Is there something I'm missing that would get past that?

Answer 8

you should recognize that all 3 triangles are similar to each other (whpalmer pointed this out)


in a right triangle, you have angle A and angle B (=90-A)
so you can label each angle as either A or B.

Answer 9

notice y is opposite angle B in the triangle on the right
and 5 is opposite angle A

in the small triangle on the left, 4 is opposite angle B
and y is opposite angle A

set up a ratio

\[ \frac{y}{5}= \frac{4}{y} \]
This is an important idea. y is the geometric mean of the two numbers
you can see (cross multiply) that y^2 = 20

now you can find x: use pythagoras