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Find the value of x in the figure below if RE is parallel to PM.

A. 14.4 units
B. 5 units
C. 7.2 units
D. 9 units

Find the value of x in the figure below if RE is parallel to PM A 144 units B 5 units C 72 units D 9 units class=

Respuesta :

calculista

Answer:

Option C. 7.2 units

Step-by-step explanation:

we know that

triangle PAM is similar to triangle RAE by AA Similarity Theorem

Remember that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

so

[tex]\frac{PA}{RA}=\frac{AM}{AE}[/tex]

substitute the given values

[tex]\frac{20+x}{20}=\frac{25+9}{25}[/tex]

solve for x

[tex]\frac{20+x}{20}=\frac{34}{25}[/tex]

[tex]20+x=\frac{34}{25}(20)[/tex]

[tex]x=\frac{34}{25}(20)-20[/tex]

[tex]x=7.2\ units[/tex]

The value of 'x' is 7.2 units and this can be determined by using the properties of the triangle and also by using the arithmetic operations.

Given :

  • RE is parallel to PM
  • RA = 20
  • AE = 25
  • RP = x
  • ME = 9

According to the given data, the side RE is parallel to side PM therefore it can be said that:

[tex]\rm \dfrac{PA}{RA}=\dfrac{MA}{EA}[/tex]

Now, substitute the values of PA, MA, RA, and EA in the above expression.

[tex]\rm \dfrac{x+20}{20}=\dfrac{9+25}{25}[/tex]

Cross multiply in the above equation.

[tex]25 \times (x + 20) = 20\times (34)[/tex]

25x + 500 = 680

Subtract 680 by 500 in the above equation.

25x = 180

DIvide 180 by 25 in the above equation.

x = 7.2

Therefore, the correct option is C).

For more information, refer to the link given below

https://brainly.com/question/19237987

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