Question

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

[3 marks]

Answer 1

(i) In parallelogram GUNS,
GS=UN [Opposite sides of parallelogram are equal]
[0.5 mark]
$\Rightarrow 3x=18\Rightarrow x=\frac{18}{3}=6cm$
[0.5 mark]
Also GU=SN [Opposite sides of parallelogram are equal]
$\Rightarrow 3y-1=26\Rightarrow 3y=26+1\Rightarrow 3y=27\Rightarrow y=\frac{27}{3}=9cm$
[0.5 mark]
Hence, x = 6 cm and y = 9 cm.

(ii) In parallelogram RUNS,
$y+7=20$ [Diagonals of a parallelogram bisects each other]
[0.5 mark]
$\Rightarrow y=20-7=13cm$
[0.5 mark]
Similarly, $x+y=16cm\Rightarrow x+13=16\Rightarrow x=16-13$
$\Rightarrow x=3cm$
[0.5 mark]
Hence, $x=3cm$ and $y=13cm$.