Question

Find the value of x and y in the following rectangle.

A. \[x = 7,y = - 8\]

B. \[x = 1,y = - 5\]

C. \[x = 2,y = 0\]

D. \[x = 1,y = 4\]

Answer 1

Hint: The length of opposite sides of a rectangle are equal.Try to form an equation using this property and then solve the linear equation of two variables using any method.

Complete step-by-step answer:
If we try to equate the opposite sides of the rectangle we will get it as
\[\begin{array}{l}
x + 3y = 13........................(i)\\
3x + y = 7..........................(ii)
\end{array}\]
Now let's try to solve this system of linear equation by elimination method,
For performing elimination method either coefficient of x or coefficient of y must be equal
Hence it is observed that none of them are equal. In order to make anyone of them equal we can either multiply the first equation by 3 which can convert the coefficient of x to be equal in both the equation or we can multiply the second equation by 3 which can convert the coefficient of y in both the equation
For instance let us multiply the first equation with 3 so that will become
\[x + 3y = 13........................(i) \times 3\]
Which will eventually become
\[3x + 9y = 39........................(iii)\]
 Now by subtracting equation (ii) from (iii)
We get,
\[\begin{array}{l}
(iii) - (ii)\\
 \Rightarrow 3x + 9y - (3x + y) = 39 - 7\\
 \Rightarrow 3x + 9y - 3x - y = 32\\
 \Rightarrow 8y = 32\\
 \Rightarrow y = 4
\end{array}\]
Now putting the value of y in the equation (i)
We get,
\[\begin{array}{l}
 \Rightarrow x + 3y = 13\\
 \Rightarrow x + 3 \times 4 = 13\\
 \Rightarrow x = 13 - 12\\
 \Rightarrow x = 1
\end{array}\]
 Therefore \[x = 1\& y = 4\] which means option D is correct.

Note: We have used elimination method to find the value of x and y, it can also be done by using substitution method where you can bring the value of x in terms of y in anyone of the equation or vice versa and then put it in the other one which will result in getting a third equation where there can be only one variable either x or y. Then, we can find the value of that variable and put it in anyone of the two equations given which will ultimately give the value of the second variable.