Question

On increasing each side of a square by 25% the increase in area will be

Answer 1

Let the side is the square be 'a'
Area = a^2
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New side
= a+ 25% of a
= a + (25/100)a
= a + (1/4)a
= (5/4) a
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New Area
= (5/4) a × (5/4) a
= (25/16) a^2
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Chance in area
= (25/16) a^2 - a^2
= (9/16) a^2
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Percentage Increase in area
={ (9/16)a^2 ÷ a^2 } × 100
= (9/16)×100
= (9×25)/4
= 56.25 %
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Answer 2

Answer:

The increase in area will be 56.25%.

Step-by-step explanation:

Given : On increasing each side of a square by 25%.

To find : The increase in area will be ?

Solution :

Let the side of the square be 's'

The area of the square is $A=s^2$

On increasing each side of a square by 25%.

The new side is $s_n=s+25\%\text{ of }s$

$s_n=s+0.25s$

$s_n=1.25s$

New area of the square is

$A_n=(1.25s)^2$

$A_n=1.5625s^2$

The change in the area is given by,

$A_c=A_n-A$

$A_c=1.5625s^2-s^2$

$A_c=0.5625s^2$

Percentage Increase in area is given by,

$A_i=\frac{A_c}{A}\times 100$

$A_i=\frac{0.5625s^2}{s^2}\times 100$

$A_i=0.5625\times 100$

$A_i=56.25\%$

Therefore, The increase in area will be 56.25%.