Question

If the sides of a square are increased by 20%, by what percentage does the area of the square increase?

Answer 1

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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