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In the diagram, △NPQ ∼ △NLM and PL = 8.

a. Find the value of x
b. Find the lengths NP and NL, rounding to the nearest hundredth.
NP =
and NL =

In The Diagram NPQ NLM And PL 8 A Find The Value Of X B Find The Lengths NP And NL Rounding To The Nearest Hundredth NP And NL class=

Sagot :

abidemiokin

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).

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

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