The value of x is 50.6 cm
Explanation:
It is given that MN = 46.2 cm, AN = 14 cm, MP = 72.6 cm and MB = x
By side splitter theorem, we have,
[tex]\frac{MA}{AN} =\frac{MB}{BP}[/tex]
Substituting the values, we have,
[tex]\frac{32.2}{14} =\frac{x}{72.6-x}[/tex]
Multiplying both sides by [tex]72.6-x[/tex], we get,
[tex]\frac{(72.6-x)32.2}{14} =x[/tex]
Multiplying, we get,
[tex]\frac{2337.72-32.2x}{14} =x[/tex]
Multiplying both sides by 14, we have,
[tex]2337.72-32.2x=14x[/tex]
Adding both sides by 32.2x, we get,
[tex]2337.72=46.2x[/tex]
Dividing both sides by 46.2, we have,
[tex]x=50.6[/tex]
Thus, the value of x is 50.6
