Question

the length ofca rectangle is twice that of its breadth. if the length of the rectangle is increased by 20% while its breadth is decreased by 20%, determine the percentage change ,if any ,in its perimeter.​

Answer 1

Step-by-step explanation:

For a rectangle, the opposite sides need to be equal and diagonals also have to be equal.

Now by using

Distance Formula =

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

Here coordinates of A are x

1

and y

1

and coordinates of B are x

2

and y

2

Similarly for other coordinates also.

Length AB=

(−2+4)

2

+(−4+1)

2

=

13

Length BC=

(4+2)

2

+(0+4)

2

=

52

Length CD=

(2−4)

2

+(3−0)

2

=

13

Length DA=

(−4−2)

2

+(−1+3)

2

=

52

Diagonal AC=

(4+4)

2

+(0+1)

2

=

65

Diagonal BD=

(2+2)

2

+(3+4)

2

=

65

ABCD are the vertices of a rectangle since AB=DC and AD=BC, also diagonal AC=BD.