Respuesta :

calculista

see the attached figure with letter to better understand the problem

we know that

The triangle MNR is a right triangle

Applying the Pythagorean Theorem

[tex]MN^{2} =MR^{2}+NR^{2}[/tex]

Solve for MR

[tex]MR^{2}=MN^{2}-NR^{2}[/tex]

in this problem we have

[tex]MN=10\ units\\NR=6\ units[/tex]

substitute the values

[tex]MR^{2}=10^{2}-6^{2}[/tex]

[tex]MR^{2}=64[/tex]

[tex]MR=8\ units[/tex]

Find the length of MQ

[tex]MQ=MR+RQ[/tex]

we have

[tex]MR=8\ units\\RQ=NP=3\ units[/tex]

substitute

[tex]MQ=8+3=11\ units[/tex]

therefore

the answer is

[tex]MQ=11\ units[/tex]


Ver imagen calculista

For the quadrilateral MNPQ, the length of MQ is 11 units.

Option C is the correct answer.

What is a Quadrilateral?

A quadrilateral can be defined as a shape that has four sides and four angles.

For the given quadrilateral, MN = 10, NP = 3, QP = 6 and [tex]\angle PQM = 90 ^\circ[/tex].

Let us consider a point L on the line MQ, as shown in the attachment. Then LQ = 3, LN= 6 and [tex]\angle NLM = 90^\circ[/tex].

Applying the Pythagoras theorem in the triangle LMN.

[tex](MN)^2 = (LN)^2 + (LM)^2[/tex]

[tex]10^2 = 6^2 + (LM)^2[/tex]

[tex]LM = \sqrt{ 100 -36}[/tex]

[tex]LM = 8[/tex]

The length of MQ can be calculated as given below.

MQ = LM + LQ

MQ = 8 + 3

MQ = 11 units.

Hence we can conclude that the length of MQ is 11 units. Option C is the correct answer.

To know more about the Pythagoras theorem, follow the link given below.

https://brainly.com/question/10174253.

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