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Question

The perimeter of a rectangle is 20cm and the difference between its length and breadth is 4cm.
Find the length and breadth of the rectangle.

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Solution

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
xy=4-------------(2)
Now,
solving equation (1),(2) by using determinant method
2(x+y)=20 -------------(1)

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

D=1111=1×1(1)×1
=1+1
=2

Dx=41101=4×1(1)×10
=4+10
=14

Now,
Dy=14110=1×101×4
=104
=6
Again,

x=(Dx)D and y=(Dy)D

So, x=(14)2=7 and y=(6)2=3

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

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