What is the percentage increase in the area of square if each of its sides is increased by 10%?

A. 10%

B. 21%

C. 44%

D. 100%

Solution(By Examveda Team)

Let the original length of sides be x
Then, new length :
$$\eqalign{ & = \left( {110\% {\text{ of }}x} \right) \cr & = \frac{{11x}}{{10}} \cr} $$
Original area $${x^2}$$
New area :
$$\eqalign{ & = {\left( {\frac{{11x}}{{10}}} \right)^2} \cr & = \frac{{121{x^2}}}{{100}} \cr} $$
Increase in area :
$$\eqalign{ & = \left( {\frac{{121{x^2}}}{{100}} - {x^2}} \right) \cr & = \frac{{21{x^2}}}{{100}} \cr} $$
∴ Increase % :
$$\eqalign{ & = \left( {\frac{{21{x^2}}}{{100}} \times \frac{1}{{{x^2}}} \times 100} \right)\% \cr & = 21\% \cr} $$

If each side of a square is increased by 10%, then what percentage of its area will be increased?

  1. 11%
  2. 20%
  3. 21%
  4. None of the above

Answer (Detailed Solution Below)

Option 3 : 21%

Free

Official Paper 2: Tripura TET 2019 Paper 2 (Maths & Science)

150 Questions 150 Marks 150 Mins

Given:

Side of a square increased = 10%

Formula used:
Increase = New number - Original number

% increase = (Increase/Original Number) × 100

Area of square = side2

Calculations:
Let the side of the square be a 

Area of a square with side a = a2

After increasing percentage of side a by 10% = a + 10% of a

⇒ a(1 + 10/100) = a(1 + 1/10)

⇒ a(11/10) = 11a/10

Area of the square after increasing side by a = (11a/10)2

⇒ (11a/10) × (11a/10) = 121a2/100

⇒ 1.21a2

Percentage change in area of square =[(1.21a2 - a2)/a2] × 100

⇒ [a2(1.21 - 1)/a2] × 100 = 0.21 × 100 

⇒ 21%

∴ Percentage change in area of square is 21%

Alternate Method

Percentage increase in a regular polygon = x + y + (xy/100)

In square length and breadth are same, x = y

Percentage increase = x + x + (xx/100)

⇒ 2x + x2/100 = 2 × 10 + 10 × 10/100

⇒ 20 + 1 = 21%

∴ The required percentage is 21%

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Solution

The correct option is A Let the length of side square be 10 units Its area = (10units)2 = 100 sq. units Now, sides increases by 25% New side = 10 + 10 × 24100 = 10 + 2.5 = 12.5 units. Change in area = (12.5 units)2–(10 units)2​ = 156.25 sq. units – 100 sq. units = 56.25 sq. units Percentage change = 56.25100 × 100% = 56.25%

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How much percentage area of a square will increase if its side is increased by 10%?

=0.21×100%=21%

How do you find the percentage increase of an area?

Calculating percentage increase and decrease.
work out the difference between the two numbers being compared..
divide the increase by the original number and multiply the answer by 100..
in summary: percentage increase = increase ÷ original number × 100..

What will be the percentage increase in the area of a square if its side is increased?

So % change area of new and old square=100002100×100=21%

What is the percentage increase in the area of Ractangle if each of its sides is increase by 20 %?

⇒ Percentage increase in area = 44. So, we have found the percentage increase in area as 44%.