Question

vw = ①
wx = ②
yw = ③
zx = ④
vx = ⑤
(there is a rectangle vywx with length yx = 31 and width vy = 19, diagonals vx and yw intersect at z)

Explanation:

Step1: Identify VW (side of rectangle)

In rectangle \(VYWX\), opposite sides are equal. \(VW = YX\), so \(VW = 31\)

Step2: Identify WX (side of rectangle)

In rectangle \(VYWX\), opposite sides are equal. \(WX = VY\), so \(WX = 19\)

Step3: Calculate diagonal YW

Use Pythagorean theorem for right triangle \(VYW\): \(YW = \sqrt{VY^2 + VW^2}\)
\(YW = \sqrt{19^2 + 31^2} = \sqrt{361 + 961} = \sqrt{1322} \approx 36.36\)

Step4: Find ZX (half the diagonal)

In rectangles, diagonals bisect each other, so \(ZX = \frac{YW}{2}\)
\(ZX = \frac{\sqrt{1322}}{2} \approx 18.18\)

Step5: Identify diagonal VX

In rectangles, diagonals are equal, so \(VX = YW\)
\(VX = \sqrt{1322} \approx 36.36\)

Answer:

1. \(VW = 31\)
2. \(WX = 19\)
3. \(YW = \sqrt{1322} \approx 36.36\)
4. \(ZX = \frac{\sqrt{1322}}{2} \approx 18.18\)
5. \(VX = \sqrt{1322} \approx 36.36\)