Question

Find the values of $x$ and $y$ in the following rectangle.

[2 Marks]

Answer 1

Since ABCD is a rectangle, opposite sides will be equal.

$\Rightarrow$ CD = AB and AD = BC

$\Rightarrow x+3y=13$ ...(i)

$\Rightarrow 3x+y=7$ ...(ii) [0.5 Marks]

On multiplying equation (i) by 3 we get,

$3x+9y=39$ ...(iii)

On subtracting equation (ii) from (iii), we get

$8y=32$

$\Rightarrow y=4$ [0.5 Marks]

On substituting $y=4$ in equation (i), we get

$x+3\left(4\right)=13$

$\Rightarrow x=1$

$\therefore$ The values of x and y are 1 and 4 respectively.
[1 Mark]