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.