Answer:
[tex]Length = 98[/tex]
Step-by-step explanation:
Given
[tex]AO = 5x - 1[/tex]
[tex]BO = 4x + 9[/tex]
Required:
The length of the diagonal
Since AO and BO are diagonals that meets at O, we have:
[tex]AO=BO[/tex]
This gives
[tex]5x - 1 = 4x + 9[/tex]
Collect Like Terms
[tex]5x - 4x = 1 + 9[/tex]
[tex]x = 10[/tex]
Subsitute 10 for x in [tex]AO = 5x - 1[/tex]
[tex]AO = 5 * 10 - 1[/tex]
[tex]AO = 50 - 1[/tex]
[tex]AO = 49[/tex]
The length of the diameter is:
[tex]Length = AO * 2[/tex]
[tex]Length = 49 * 2[/tex]
[tex]Length = 98[/tex]
