Solution:

To solve this problem, we need to understand the relationship between the side length and the area of a square. The area of a square is given by the formula:

A = s^2

Where A represents the area and s represents the side length of the square.

Step 1: Find the percentage increase in the side length

The problem states that the sides of the square are increased by 35%. Let's say the original side length of the square is 'x'. To find the increased side length, we need to add 35% of 'x' to 'x':

Increased side length = x + 35% of x

Step 2: Calculate the increased side length

To calculate the increased side length, we need to convert 35% to a decimal by dividing it by 100:

35% = 35/100 = 0.35

Now, we can calculate the increased side length:

Increased side length = x + 0.35x

Simplifying the expression, we get:

Increased side length = 1.35x

Step 3: Find the new area of the square

To find the new area of the square, we substitute the increased side length into the area formula:

New area = (1.35x)^2

Expanding and simplifying the expression, we get:

New area = 1.8225x^2

Step 4: Calculate the percentage increase in the area

To calculate the percentage increase in the area, we need to find the difference between the new area and the original area, divide it by the original area, and multiply by 100:

Percentage increase = (New area - Original area) / Original area * 100

Substituting the values, we get:

Percentage increase = (1.8225x^2 - x^2) / x^2 * 100

Simplifying the expression, we get:

Percentage increase = 0.8225 * 100

Percentage increase = 82.25%

Therefore, the area of the square increases by 82.25% when the sides are increased by 35%.

Since diagonal = 2​a
If the diagonal increased by 35%, then a also increases by 35%.
Therefore, a′=a+0.35a=(1.35)a
∴(a′)2=(1.35a)2=1.8255  a2
∴ Change =0.8225a2
∴ Increase in area =82.25%.
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