The length and the breadth of a rectangle are increased by 15% and 10%, respectively. What is the percentage increase in the area of the rectangle?

Let's assume the initial length and the breadth of a rectangle are '10y' and '10z' respectively.

Area of a rectangle initially = length $$\times$$ breadth

= $$10y\times10z$$

= 100yz

The length and the breadth of a rectangle are increased by 15% and 10%, respectively.

New length = 10y of (100+15)%

= 10y of 115%

= $$10y\times\frac{115}{100}$$

= 11.5y

New breadth = 10z of (100+10)%

= 10z of 110%

= $$10z\times\frac{110}{100}$$

= 11z

New area of a rectangle = 11.5y $$\times$$ 11z = 126.5yz

Percentage increase in the area of the rectangle = $$\frac{\left(126.5yz-100yz\right)\times\ 100}{100yz}$$

= $$\frac{\left(26.5yz\right)\times\ 100}{100yz}$$

= 26.5%

Short cut ::

Successive percentage increase = $$15\%+10\%+\frac{\left(15\times\ 10\right)\%}{100}$$

= $$15\%+10\%+\frac{\left(150\right)\%}{100}$$

= $$15\%+10\%+1.5\%$$

= 26.5%