Question

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

Explanation:

Step1: Identify Square Properties

In square QRST, all sides are equal, and diagonals are equal and bisect each other. Let's assume the side length of the square is \( s \). The diagonals of a square are \( s\sqrt{2} \), and since diagonals bisect each other, \( RV = VS = \frac{s\sqrt{2}}{2}=\frac{s}{\sqrt{2}} \), and \( RS = s \).

Step2: Perimeter Formula for Triangle

Perimeter of \( \triangle RVS \) is \( RV + VS + RS \). Substituting the values, if we assume the side length of the square (e.g., let's say \( s = 10 \) for example, since the problem might have a standard side length, but since it's not given, maybe a typo or missing info. Wait, maybe the square has side length, say, 8 (common problem). Wait, maybe the original problem had a side length. Since it's missing, but assuming a side length (let's correct: maybe the square has side length \( a \). Then diagonal \( d = a\sqrt{2} \), so \( RV = VS = \frac{d}{2}=\frac{a\sqrt{2}}{2} \), \( RS = a \). So perimeter \( P = \frac{a\sqrt{2}}{2}+\frac{a\sqrt{2}}{2}+a = a\sqrt{2}+a = a(1 + \sqrt{2}) \). If \( a = 10 \), then \( P = 10(1 + 1.414) = 24.14 \approx 24.1 \). But since the problem is incomplete (no side length), but maybe in the original problem, the square has side length, say, 8. Wait, maybe the user missed the side length. Alternatively, maybe the square is, for example, with side 6. Wait, perhaps the problem had a side length, like 10. Let's assume side length \( a = 10 \). Then \( RV = VS = \frac{10\sqrt{2}}{2}=5\sqrt{2}\approx7.07 \), \( RS = 10 \). Perimeter \( = 7.07 + 7.07 + 10 = 24.14 \approx 24.1 \).

Answer:

(Assuming side length of square is 10, the perimeter is) \( \boxed{24.1} \) (Note: This answer depends on the side length of the square. If the side length is different, recalculate with \( P = a(1 + \sqrt{2}) \) where \( a \) is the side length of the square.)