Geometry: An Interactive Journey to Mastery

Solutions

3. ,IWKHVLGHVRIWKHUHFWDQJOHFRPHLQDUDWLRWKHQWKHVLGHOHQJWKV
   are 4x and 3x for some value x, as shown in Figure S.5.3.
   :HKDYHWKHIROORZLQJ
   
   
   
    



 

 



.

xx

xx

x

x

x





6RWKHOHQJWKDQGZLGWKRIWKHUHFWDQJOHDUH^63 and^84.

4. Label the remaining side h, as shown in Figure S.5.4.
   D௘ͽ %\WKH3\WKDJRUHDQWKHRUHP
   
   

9

9 more

9

3.

ah

a

a

a





!

!

E௘ͽ %\WKH3\WKDJRUHDQWKHRUHP

 





bh

b

b



!

!

F௘ͽ b h, which is obviously larger than 9 + h = aͼ௘EHFDXVHLVODUJHUWKDQ௘ͽ

Thus, b! a. This gives b! a.

h a b

32

Figure S.5.4

4 x

3 x^21

Figure S.5.3