Question

80 POINTS AND BRAINLIEST

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

Answer 1

Answer: $x=50.6$

Step-by-step explanation:

 According to the Side Splitter Theorem, when a line is parallel to a side of a triangle and it intersects the other two sides, these sides are divided proportionally.

Based on this, you can write the following proportion:

$\frac{MA}{AN}=\frac{MB}{BP}$

Observing the figure  given in the exercise, you can identify that:

$MA=46.2-14=32.2\\\\AN=14\ cm\\\\MB=x\\\\BP=72.6-x$

Finally, you must substitute values into  $\frac{MA}{AN}=\frac{MB}{BP}$ and solve for "x" in order to find its value. This is:

$\frac{32.2}{14}=\frac{x}{72.6-x}\\\\2.3=\frac{x}{72.6-x}\\\\(2.3)(72.6-x)=x\\\\166.98-2.3x=x\\\\166.98=x+2.3x\\\\\frac{166.98}{3.3}=x\\\\x=50.6$