Question

Circle G and circle U are similar. Find the value of X

A.
5
B.
15
C.
60
D.
240

Answer 1

Hello!

First you have to find what they did to get the second triangle

20 / 3 = 6.666...

6.666... / 4 = 1.666...

The multiplied the first circle by 1.666... to get the second circle

Multiply where x is in the first circle

9 * 1.6666 = 14.999

Round this to 15

The answer is B) 15

Hope this helps!

Answer 2

since they are similar, their radius:angles ratio will be the same so set up a proportion:
$\frac{20\pi}{3} \div 4\pi = \frac{x}{9} \\ crossmultiply \\ 4\pi \times x = \frac{20\pi}{3} \times \frac{9}{1}$
$4\pi \times x = \frac{20\pi}{1} \times \frac{3}{1} \\ 4\pi \times x = 60\pi \\ \frac{4\pi \: x}{4\pi} = \frac{60\pi}{4\pi} \\ x = 15$
B) 15 is your final answer