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NNADVOKAT [17]
3 years ago
7

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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