Question

Find the length of AG

Answer 1

`AG=22`

Explanation:

Follow the next steps:

`(A-B)/(A-E) =(B-C)/(E-F) =(C-D)/(F-G) =(A-C)/(A-F) =(B-D)/(E-G) =(A-D)/(A-G)`

Let:

`(A-B)/(A-E) =(B-C)/(E-F)\\ \\(4)/(A-E) =(5)/(10x)\\ \\Solving\hspace{3}for\hspace{3}A-E\\\\A-E=8x`

Now:

`(C-D)/(F-G) =(A-C)/(A-F) \\\\(2)/(F-G) =(9)/(18x) \\\\Solving\hspace{3}for\hspace{3}F-G\\\\F-G=4x`

Hence:

`A-G=(A-E)+(E-F)+(F-G)=22x`

Finally:

`(B-D)/(E-G) =(A-D)/(A-G)\\\\(A-D)/(B-D) =(A-G)/(E-G)\\`

`(11)/(7) =(22x)/(14x) \\\\(11x^(2) )/(7) -(11)/(7) =0\\\\`

Hence:

`x=1\\x=-1`

Since it would be absurd for
`x=-1`, the real solution is
`x=1`

Therefore:

`AG=22`