Question

find the perimeter of $\triangle rvs$ for square qrst.
the perimeter of $\triangle rvs$ is \square.
(type an integer or decimal rounded to one decimal place as needed.)

Explanation:

Step1: Identify square side length

Side length of square $QRST$: $RS = QR = 5$

Step2: Calculate diagonal length

Diagonal of square: $QS = RT = 5\sqrt{2} \approx 7.071$. Diagonals of square bisect each other, so $RV = SV = \frac{5\sqrt{2}}{2} \approx 3.536$

Step3: Sum sides for perimeter

Perimeter of $\triangle RVS$: $RS + RV + SV$
$\approx 5 + 3.536 + 3.536$

Answer:

12.1