Question

What is the value of x? Enter your answer, as a decimal, in the box.

Answer 1

Answer:

$x=50.6\text{ cm}$

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 $\Delta NMP\sim \Delta AMB$.

Since we know that corresponding sides of similar triangles are proportional, so we can set up a proportion as:

$\frac{MA}{MN}=\frac{x}{MP}$    

We can see from our given diagram that $MA=MN-AN$.

Upon substituting our given values we will get,

$MA=46.2\text{ cm}-14\text{ cm}$

$MA=32.2\text{ cm}$  

Now let us substitute our given side length in the above proportion.

$\frac{32.2}{46.2}=\frac{x}{72.6}$

Upon multiplying both sides of our equation by 72.6 we will get,

$\frac{32.2}{46.2}*72.6=\frac{x}{72.6}*72.6$

$50.6=x$

Therefore, the value of x is 50.6 cm.