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, side length \( RQ = 11 \) (assuming the red label is 11). Diagonals of a square are equal and bisect each other at 90°? No, bisect at 90°? Wait, diagonals of a square are equal, length \( d = s\sqrt{2} \), and they bisect each other, so \( RV = SV = \frac{d}{2} \), and \( RS = s = 11 \).

First, find diagonal length: \( RT = RQ\sqrt{2} = 11\sqrt{2} \approx 15.556 \). Then, since diagonals bisect each other, \( RV = SV = \frac{11\sqrt{2}}{2} \approx 7.778 \).

Step2: Calculate perimeter of \( \triangle RVS \)

Perimeter \( P = RS + RV + SV \). \( RS = 11 \), \( RV \approx 7.778 \), \( SV \approx 7.778 \). So \( P = 11 + 7.778 + 7.778 \approx 26.556 \), rounded to one decimal: \( 26.6 \)? Wait, wait, maybe I misread the side. Wait, the square has side 11? Let's recheck.

Wait, in square QRST, sides are equal. So \( RQ = 11 \), so \( RS = 11 \) (since it's a square, all sides are 11). Diagonals: \( RT \) and \( QS \) are diagonals, length \( 11\sqrt{2} \). Then \( V \) is the intersection, so \( RV = \frac{11\sqrt{2}}{2} \), \( SV = \frac{11\sqrt{2}}{2} \).

So perimeter: \( 11 + 2 \times \frac{11\sqrt{2}}{2} = 11 + 11\sqrt{2} \approx 11 + 15.556 = 26.556 \approx 26.6 \). Wait, but maybe the side is 11, so let's compute \( 11\sqrt{2} \approx 15.556 \), then half is \( 7.778 \), so two of those: \( 15.556 \), plus 11: \( 26.556 \approx 26.6 \).

Wait, maybe the original side is 11 (the red number). Let's confirm:

Diagonal of square: \( s\sqrt{2} \), so for \( s = 11 \), diagonal \( 11\sqrt{2} \approx 15.556 \). Diagonals bisect each other, so \( RV = SV = \frac{11\sqrt{2}}{2} \approx 7.778 \). Then perimeter: \( 11 + 7.778 + 7.778 = 26.556 \approx 26.6 \) (rounded to one decimal).

Answer:

\boxed{26.6} (assuming side length is 11; if the side was different, adjust, but based on the image's red label as 11, this is the result)