Question

question
triangle uvw is formed by connecting the mid - points of the side of triangle rst. the lengths of the sides of triangle rst are shown. what is the length of wv? figures not necessarily drawn to scale.
answer attempt 1 out of 2
wv =

Explanation:

Step1: Recall mid - point theorem

The line segment joining the mid - points of two sides of a triangle is parallel to the third side and half its length.

Step2: Identify right - triangle in $\triangle RST$

In $\triangle RST$, by the Pythagorean theorem, if the two legs of $\triangle RST$ are $a = 4$ and $b = 4$, and the hypotenuse is $RT$. Then $RT=\sqrt{4^{2}+4^{2}}=\sqrt{16 + 16}=\sqrt{32}=4\sqrt{2}$. Also, since $\triangle UVW$ is formed by mid - points of $\triangle RST$, we can use another approach. Consider the right - triangle formed in $\triangle RST$ with legs $4$ and $6$.

Step3: Apply Pythagorean theorem to find $WV$

In the right - triangle formed by the segments related to $\triangle RST$, if we consider the two segments of lengths $3$ (half of $6$) and $4$ (half of $8$) related to the sides of $\triangle RST$ that $WV$ is part of. By the Pythagorean theorem $WV=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5$.

Answer:

$5$