Question

The diagram shows quadrilateral MNPQ.

Answer 1

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

$MN^{2} =MR^{2}+NR^{2}$

Solve for MR

$MR^{2}=MN^{2}-NR^{2}$

in this problem we have

$MN=10\ units\\NR=6\ units$

substitute the values

$MR^{2}=10^{2}-6^{2}$

$MR^{2}=64$

$MR=8\ units$

Find the length of MQ

$MQ=MR+RQ$

we have

$MR=8\ units\\RQ=NP=3\ units$

substitute

$MQ=8+3=11\ units$

therefore

the answer is

$MQ=11\ units$

Answer 2

11 units wil be your answer.here you have to draw a line from n and it will  fall line mq.now by pythagorus theorem solve it and 3 to it