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?
- 11%
- 20%
- 21%
- 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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