The lengths of 2 adjacent sides of a square are increased by 35% and 25%. The area of the resulting rectangle exceeds the area of the square by:

Two adjacent sides of a square are increased by 35% and 25%.

The area of a square with side length s is $$s^2.$$​​

Area of rectangle = length × breadth

The percentage increase in the area can be found using the formula for successive percentage changes:

Percentage increase in area = $$\left(x + y + \frac{x \times y}{100}\right)$$​​

Let the side of the original square be s.
The area of the square is:

\text{Area of square} = $$s^2$$​​

After increasing the sides by 35% and 25%, the new dimensions of the rectangle are:

​$$\text{New length} = s \times \left(1 + \frac{35}{100}\right) = s \times 1.35 \\$$​​

​$$\text{New width} = s \times \left(1 + \frac{25}{100}\right) = s \times 1.25$$​​

The area of the resulting rectangle is:

​$$\text{Area of rectangle} = \left(s \times 1.35\right) \times \left(s \times 1.25\right) = s^2 \times 1.35 \times 1.25\\$$​​

​$$\text{Area of rectangle} = s^2 \times 1.6875$$​​

Now, the percentage increase in the area is:

​$$\text{Increase in area} = 1.6875 \times 100\% - 100\% = 68.75\%$$​​

Thus, the area of the resulting rectangle exceeds the area of the original square by 68.75%. 

​Percentage increase in area = $$\left(x + y + \frac{x \times y}{100}\right)$$ 

Using the value; 

​$$\begin{aligned}&\left(35 + 25 + \frac{35 \times 25}{100}\right) \\&= 68.75\% \end{aligned}$$      ​