You still need to use some algebra here. Percentage alone does not make the cut unless you know how to use percentage on its own.

I will use "units" to represent algebraic letters (something like u or x).

Q47

Let the length of the rectangle be 20 units and the breadth of the rectangle be 10 units.

Perimeter of original rectangle
= 20 + 10 + 20 + 10
= 60 units

What happens after the dimensions of the rectangle are changed?

Increase in length = 20% x 20 = 4 units
New length = 20 + 4 = 24 units

Decrease in breadth = 20% x 10 = 2 units
New breadth = 10 - 2 = 8 units

New perimeter
= 24 + 8 + 24 + 8
= 64 units

This is an increase of 4 units from before.

Percentage increase
= 4/60 x 100%
= 6 2/3...% (when placed as a mixed fraction)
~ 6.67% (when placed as a decimal to 3 significant figures - yes you have learnt significant figures by now)

Q48

Let the length of each side of a square be 10 units.

[Next time, please use 10x or 10u rather than 10 units]

Current area of square
= 10 units x 10 units
= 100 units²

Increase in side = 20% x 10 = 2 units
New side = 10 + 2 = 12 units

Area of new square
= 12 units x 12 units
= 144 units²

Increase in area
= 44 units²

Percentage increase in area
= 44/100 x 100%
= 44%