Question

question 4. multiple choice (worth 1 points) (05.01 mc) in △pqr, what is the length of segment qr? o 22√3 o 11 o 11√2 o 22√2

Explanation:

Step1: Identify triangle type

Since two angles are 45° and one is 90°, it's a 45 - 45- 90 right - triangle. In a 45 - 45- 90 triangle, the ratio of the sides is $1:1:\sqrt{2}$, where the hypotenuse $c$ is related to the legs $a$ and $b$ (equal in this case) by $c = a\sqrt{2}$.

Step2: Set up the equation

Let the length of $QR=a$ and the hypotenuse $PR = 22$. Using the 45 - 45- 90 triangle ratio $PR=a\sqrt{2}$. So, $22=a\sqrt{2}$.

Step3: Solve for $a$

To find $a$, we solve the equation $22=a\sqrt{2}$ for $a$. Divide both sides by $\sqrt{2}$: $a=\frac{22}{\sqrt{2}}$. Rationalize the denominator by multiplying the numerator and denominator by $\sqrt{2}$: $a=\frac{22\sqrt{2}}{2}=11\sqrt{2}$.

Answer:

C. $11\sqrt{2}$