Answer:
x = 14
NP = 3.66
NL = 8.01
Step-by-step explanation:
since △NPQ ∼ △NLM
<L = <P
3x + 18 = 60
3x = 60 - 18
3x = 42
x = 42/3
x = 14
Similarly;
PN/PL = QN/QM
y/8 = 3.2/7
Cross multiply
7y = 3.2* 8
7y = 25.6
y = 25.6/7
y = 3.66
Hence NP = 3.66
Also
NP/NQ = NL/NM
3.66/3.2 = NL/7
3.2NL = 7 * 3.66
3.2NL = 25.62
NL = 25.62/3.2
NL = 8.01
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).
The given tingle NPQ and triangle NLM are the similar triangle.
The length of the line PL is 8 cm.
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
