Question

A square is converted into a rectangle by increasing one of its sides by 5% and reducing the other by
5% What will be the percentage change in the area of the two figures?​

Answer 1

⇒%age=a+b+ab100

If increment, consider positive sign else negative sign.

%age=−5+5+(−5)(5)100

%age=0+−25100=−25%

Therefore, percentage change in the area of rectangle is {math] - 25\% [/math] which means area is decreased by {math] 25\% [/math]

Answer 2

Concept :

The measurement that expresses the size of a region on a plane or curved surface is called area. As opposed to surface area, which refers to the area of an extended surface or the perimeter of a three-dimensional object, plane section or plane surface refers to the circumference of a form or planar lamina.

Given:

A square is converted into a rectangle by increasing one of its sides by 5% and reducing the other by $5$%.

Find:

The percentage change in the area of the two figures.

Solution:

According to the problem,

Let, the side of the square is $x$.

So, the area is $x^2$

A square is converted into a rectangle by increasing one of its sides by 5% and reducing the other by 5%

So, the sides of the rectangle are =$( x + 5x/100) = (x + x/20) = 21x/20$

and $( x- 5x/100) = (x - x/20 ) = 19x/20$

So, the new area is = $399 x^2/400$

Change in area is = $( x^2-399x^2/400) = x^2/400$

So, the change in area is $25$%

Hence the change in area is $25$%

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