Question

the diagram shows quadrilateral mnpq. what is the length of line segment mq? 8 units 10 units 11 units 15 units

Explanation:

Step1: Apply the Pythagorean theorem in right - triangle formed

In the right - triangle with hypotenuse $MN = 10$ and one leg $NP = 6$. Let the other leg be $x$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 10$ and $a = 6$. Then $x=\sqrt{10^{2}-6^{2}}$.

Step2: Calculate the value of $x$

$x=\sqrt{100 - 36}=\sqrt{64}=8$.

Step3: Find the length of $MQ$

The length of $MQ$ is equal to the length of the horizontal segment which is the same as the length of the non - vertical leg of the right - triangle we just considered. So $MQ = 8$ units.

Answer:

8 units