Question

Find the values of $x$ and $y$ in the following rectangle [see Figure].

Answer 1

Step $1$: Evaluate the value of $y$.

We know that, for a rectangle, opposite sides are equal. So,

$$\begin{gathered} x+3y=13 \\ \Rightarrow x=13-3y.....\left(1\right) \end{gathered}$$

and $3x+y=7.....\left(2\right)$

Substitute the value of $x$ in equation $\left(2\right)$. So,

$\Rightarrow 3\left(13-3y\right)+y=7$

$\Rightarrow$ $39-9y+y=7$

$\Rightarrow$ $-8y=-32$

$\Rightarrow$ $y=4$

Step $2$: Evaluate the value of $x$.

Next, substitute the value of $y$ in equation $\left(1\right)$. So

$\Rightarrow x=13-3\left(4\right)$

$\Rightarrow$$x=13-12$

$\Rightarrow x=1$

Hence, the values of $x$ and $y$ in the given rectangle are $1$ and $4$ respectively.