Question

1. rt = 22 and us = 18

vt =
uv =
rs =
st =

Explanation:

Step1: Use the property of parallelogram diagonals bisecting each other

In a parallelogram, the diagonals bisect each other. So \(VT=\frac{1}{2}RT\). Given \(RT = 22\), then \(VT=\frac{22}{2}=11\).

Step2: Use the property of parallelogram diagonals bisecting each other

Since the diagonals bisect each other, \(UV=\frac{1}{2}US\). Given \(US = 18\), then \(UV=\frac{18}{2}=9\).

Step3: Use the Pythagorean theorem (assuming it's a rhombus - diagonals are perpendicular)

Let the diagonals \(RT\) and \(US\) intersect at \(V\). \(RV = VT=11\), \(UV = VS = 9\). In right - triangle \(RVS\), by the Pythagorean theorem \(RS=\sqrt{RV^{2}+VS^{2}}\). Substitute \(RV = 11\) and \(VS = 9\), we get \(RS=\sqrt{11^{2}+9^{2}}=\sqrt{121 + 81}=\sqrt{202}\approx14.21\).

Step4: Use the property of parallelogram sides

In a parallelogram, opposite sides are equal. Also, using the Pythagorean theorem in right - triangle \(VST\) (since diagonals of a rhombus are perpendicular), \(ST=\sqrt{VT^{2}+VS^{2}}\). Substitute \(VT = 11\) and \(VS = 9\), we get \(ST=\sqrt{11^{2}+9^{2}}=\sqrt{202}\approx14.21\).

Answer:

\(VT = 11\)
\(UV=9\)
\(RS=\sqrt{202}\approx14.21\)
\(ST=\sqrt{202}\approx14.21\)