Answer:
? = 7.
Step-by-step explanation:
The two triangles are similar because of the AA Theorem.
The larger triangle's side that is equal to 9 + 3 corresponds to the smaller triangle's side length of 9, while the larger triangle's 21 + ? side corresponds to the smaller triangle's 21 side. Now, we can set up a proportion!
[tex]\frac{9}{9+3} =\frac{21}{21 + ?}[/tex]
[tex]\frac{9}{12} =\frac{21}{? + 21}[/tex]
[tex]\frac{3}{4} =\frac{21}{? + 21}[/tex]
[tex]\frac{1}{4} =\frac{7}{? + 21}[/tex]
? + 21 = 7 * 4
? + 21 = 28
? = 28 - 21
? = 7
Hope this helps!
