Question

The following figures \(GUNS\) and \(RUNS\) are parallelograms. Find \(x\) and \(y\). (Lengths are in cm)

Answer 1

(i) We know that the lengths of opposite sides of a parallelogram are equal to each other.
\(\Rightarrow\) \(GU = SN\)
\(\Rightarrow\) \(3y - 1 = 26\)
\(\Rightarrow\) \(3y = 27 \)
\(\Rightarrow\) \(y = 9\)
\(\Rightarrow\) \(SG = NU\)
\(\Rightarrow\) \(3x = 18\)
\(\Rightarrow \) \(x = 6\)

Hence, the measures of \(x\) and \(y\) are \(6\) \(cm\) and \(9\) \(cm\) respectively.

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(ii) We know that the diagonals of a parallelogram bisect each other.
\(\Rightarrow\) \(y + 7 = 20\)
\(\Rightarrow\) \(y = 13\)
\(\Rightarrow\) \(x + y = 16\)
\(\Rightarrow\) \(x + 13 = 16\)
\(\Rightarrow\) \(x = 3\)

Hence, the measures of \(x\) and \(y\) are \(3\) \(cm\) and \(13\) \(cm\) respectively.