The plinth of a house has an area of 200 square metres. It is rectangular in shape and its length and breadth are in the ratio 2 : 1. The owner of the house extends the terrace by 1 m on each side. What is the percentage of area that has increased in the terrace relative to the plinth ? 

Formula used:

Area of rectangle = length× breadth

Calculation:

Let the length be 2X and the breadth be X. Then, 

Area of plinth = length x breadth

⇒  (2X)*(X)

⇒ 2x² = 200 sq. m.

⇒ X = √(100)

⇒ X = 10 m.

The dimensions of the plinth are 2X = 20 m (length) & X = 10 m (breadth).

Now, the owner extends the terrace by 1 m on each side. So, the new

dimensions of the terrace are (20 + 2) m (length) and (10 + 2) m (breadth).

Area of new terrace = (20 + 2) x (10+2)

Area of new terrace = 264 sq. m

Increase in area = 264 - 200

Increase in area = 64 sq. m

Percentage increase = (increase in area/area of plinth) x 100

Percentage increase = (64/200) x 100 = 32%

∴ The percentage increase in the area is 32%.