Two triangle are similar if they have the same ratio of the corresponding sides and equal pair of corresponding angle. The value of the x is 14 degrees, the length of the NP is 3.7 cm (round to the nearest hundred), and the length of the NL is 8 cm ( round to the nearest hundred).
Given information-
The given tingle NPQ and triangle NLM are the similar triangle.
The length of the line PL is 8 cm.
Similar triangle-
Two triangle are similar if they have the same ratio of the corresponding sides and equal pair of corresponding angle.
Value of the x-
As the two triangle are similar triangle, thus the length of the angle P is equal to the angle L. Therefore,
[tex]\angle L =\angle P\\
[/tex]
Keep the value of the angle from the diagram,
[tex]\begin{algined}\\
3x+18&=60\\
3x&=60-18\\\\
3x&=42\\
x&=\dfrac{42}{3} \\
x&=14\\
\end[/tex]
Thus the value of the x is 14.
The length of the NP.
In the similar triangle the following ratios are equal,
[tex]\dfrac{PN}{PL} =\dfrac{QN}{QM} [/tex]
Put the values from the diagram,
[tex]\begin{aligned}
\dfrac{y}{8}&=\dfrac{3.2}{7} \\
y&=\dfrac{3.2}{7} \times 8\\
y&=3.66\\
\end[/tex]
Value of y is equal to the length NP. Hence the length of the NP is equal to the 3.66 cm.
The length of the NL-
In the similar triangle the following ratios are equal,
[tex]\dfrac{NP}{NQ} =\dfrac{NL}{NM} [/tex]
Put the values from the diagram,
[tex]\begin{aligned}
\dfrac{3.66}{3.2}&=\dfrac{NL}{7} \\
NL&=\dfrac{3.66}{3.2} \times 7\\
y&=8.01\\
\end[/tex]
Thus the length of the NL is equal to the 8.01 cm.
Hence the value of the x is 14 degrees, the length of the NP is 3.7 cm (round to the nearest hundred), and the length of the NL is 8 cm ( round to the nearest hundred).
Learn more about the similar triangle here;
https://brainly.com/question/25882965
