Question

The perimeter of a rectangle is 20cm and the difference between its length and breadth is 4cm.
The length and breadth of the rectangle will respectively be ___

• A. 4cm, 3cm
• B. 7cm, 3cm
• C. 10cm, 5cm
• D. 1cm, 4cm

Answer 1

The correct option is B 7cm, 3cm

Let the length and breadth of the rectangle be x cm and y cm repectively
So, as per the first condition
$2(x+y)=20$ -------------(1)
Again,
as per the second condition
$x-y=4$-------------(2)
Now,
solving equation (1),(2) by using determinant method
$2(x+y)=20$ -------------(1)

$x+y=10$
$x-y=4$-------------(2)

$D=\left|\begin{array}{cc}1& -1\\ 1& 1\end{array}\right|=1\times 1-(-1)\times 1$
$=1+1$
$=2$

$D_x=\left|\begin{array}{cc}4& -1\\ 10& 1\end{array}\right|=4\times 1-(-1)\times 10$
$=4+10$
$=14$

Now,
$D_y=\left|\begin{array}{cc}1& 4\\ 1& 10\end{array}\right|=1\times 10-1\times 4$
$=10-4$
$=6$
Again,

$x=\frac{\left(D_x\right)}{D}$ and $y=\frac{\left(D_y\right)}{D}$

So, $x=\frac{\left(14\right)}{2}=7$ and $y=\frac{\left(6\right)}{2}=3$

Hence the length and breadth of the rectangle are 7cm and 3cm respectively.