If the sides of a square are increased by 20%, by what percentage does the area of the square increase?
Answers
Answer:
Percentage increase in area is 44%
Step-by-step explanation:
Given: square increased by 20%
To find: Percentage increase in area.
Let assume the side of a square = x
so, now increased side of a square = x + 20% x
= x + 20/100x
= x+0.2x [ 20/100=0.2]
= 1.2x
Formula of area of square= side^2
old area of square = x^2 ( when side =x)
new area of square = 1.2x^2
= 1.44x^2( when side is increased be 20% i.e. 1.2x)
Formula: Percentage change in area = new area - old area/old area
= [(1.44x^2) - (x^2)/ x^2 ]* 100
=[ x^2( 1.44 -1)/x^2]* 100{ x^2 taken outside as it is common in both}
= 1.44-1/1 * 100 [ x^2 got cancelled because x^2 was common in numerator and denominator ]
= .44 *100
=44
so the percentage change in area of the square increased is 44%.
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