Question

question 5(multiple choice worth 1 points) (05.01 mc) in △rst, what is the length of segment rt? s t 26 45° 45° r 26√3 52 13 26√2

Explanation:

Step1: Identify triangle type

Since $\angle R = 45^{\circ}$ and $\angle T=45^{\circ}$ and $\angle S = 90^{\circ}$, $\triangle RST$ is a 45 - 45- 90 right - triangle. In a 45 - 45- 90 right - triangle, the legs are congruent. Let $RS = ST = 26$ (given $RS = 26$).

Step2: Apply Pythagorean theorem

The Pythagorean theorem for a right - triangle is $a^{2}+b^{2}=c^{2}$, where $a$ and $b$ are the legs and $c$ is the hypotenuse. Here $a = 26$, $b = 26$, and we want to find the length of the hypotenuse $RT$. So $RT^{2}=RS^{2}+ST^{2}=26^{2}+26^{2}=2\times26^{2}$.

Step3: Solve for $RT$

Take the square - root of both sides: $RT=\sqrt{2\times26^{2}}=26\sqrt{2}$.

Answer:

D. $26\sqrt{2}$