80 POINTS AND BRAINLIEST

Mathematics

1 answer:

yawa3891 [41]3 years ago

6 0

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:

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

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