Answer:
[tex]x=50.6\text{ cm}[/tex]
Step-by-step explanation:
We have been given a diagram of two triangle and we are asked to find the value of x.
We can see from our diagram that triangle AMB and triangle NMP share a common angle that is angle M. As line AB is parallel to line NP, so corresponding angle will be also equal, therefore, by AAA similarity [tex]\Delta NMP\sim \Delta AMB[/tex].
Since we know that corresponding sides of similar triangles are proportional, so we can set up a proportion as:
[tex]\frac{MA}{MN}=\frac{x}{MP}[/tex]
We can see from our given diagram that [tex]MA=MN-AN[/tex].
Upon substituting our given values we will get,
[tex]MA=46.2\text{ cm}-14\text{ cm}[/tex]
[tex]MA=32.2\text{ cm}[/tex]
Now let us substitute our given side length in the above proportion.
[tex]\frac{32.2}{46.2}=\frac{x}{72.6}[/tex]
Upon multiplying both sides of our equation by 72.6 we will get,
[tex]\frac{32.2}{46.2}*72.6=\frac{x}{72.6}*72.6[/tex]
[tex]50.6=x[/tex]
Therefore, the value of x is 50.6 cm.
