Question

https://media.glynlyon.com/g_geo_2013/5/tri1.gif

a =



4

6

9

Answer 1

Use Pythagoras Theorem:
\(\Large c^2=6^2+4^2=52\)

\(\Large (4+a)^2=c^2+b^2 \Rightarrow a=\sqrt{52+b^2}-4\) (1)

\(\Large b^2=6^2+a^2 \Rightarrow a=\sqrt{b^2-36}\) (2)

From (1)(2): \(\Large \sqrt{52+b^2}-4=\sqrt{b^2-36}\\\Large \sqrt{52+b^2}=\sqrt{b^2-36}+4\\\Large 52+b^2=b^2-36+8\sqrt{b^2-36}+16\\\Large\sqrt{b^2-36}=9\\\Large b^2=9^2+36=117\)
\(\Large \Rightarrow a=\sqrt{117-36}=\sqrt{81}=9\)