Question

If the breadth of a rectangle is increased by 10 percent and the area is unchanged,then find the percentage of length to be decreased?​

Answer 1

Answer:

Length should be decreased by 100/11 % .

Step-by-step explanation:

Let us consider a rectangle with the length of l units and width ( or breadth ) be b units.

From the properties of quadrilaterals :

• Area of rectangle = length x breadth

Here,

Length of rectangle is l units and breadth is b units.

Thus,

= > Original area of the rectangle = length x breadth = l x b unit^2 = lb unit^2

When breadth of the rectangle is increased by 10% :

= > New breadth of the rectangle = b + 10% of b

= > New breadth = b ( 1 + 10% ) unit

= > New breadth = b ( 1 + 10 / 100 ) unit

= > New breadth = b ( 11 / 10 ) unit

Let the% of decrease of length be a.

= > New length = length ( 1 - a% ) = length ( 1 - a / 100 ) = length ( 100 - a ) / 100

Now,

= > Area of the rectangle = lb ( 100 - a ) ( 11 / 1000 ) unit^2

Given,

Area is unchanged.

= > Area with original breadth = area with increased breadth

= > lb = lb( 100 - a )( 11 / 1000 )

= > 1000 = 11( 100 - a )

= > 1000 = 1100 - 11a

= > 100 = 11a

= > 100 / 11 = a

Hence length should be decreased by 100/11 % .