Question

14 If the length of a rectangular field be increased by 50% and the breadth be decreased by 25%, find the % change in area: ​

Answer 1

Answer:

12.5%       (increased)

Step-by-step explanation:

Let the original length and breadth be 'x' and 'y' respectively.

∴ Area of field = length * breadth

                        = xy

When length is increased by 50% and breadth is decreased by 25%.

  New length = x + (50% of x)

                       = x + (50/100)*x

                       = 3x/2

  New breadth = y - (25% of y)

                         = y - (25/100)*y

                         = 3y/4

∴ Area of field = new length * new breadth

                        = (3x/2) * (3y/4)

                        = 9xy/8      [more than xy]

Hence,

% change = (change/original) * 100%

                 = (9xy/8 - xy)/xy * 100%

                 = (xy/8)/xy * 100%

                 = (1/8) * 100%

                 = 12.5 %

Answer 2

Let the original length and breadth be X and Y respectively .

Area of rectangular field = Length * breadth

so ,

⇒ Area = xy

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and also given that ,

• when length is increased by 50% and breadth is decreased by 25%

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New length = x + (50% of x)

= x + (50/100)x = x + (½x) = (3x/2)

➻ New Length = (3x/2)

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New Breadth = y - (25% of y)

= y - (25/100)y = y - (¼)y = (3y/4)

➻ New Breadth = (3y/4)

_____________________________

Area of field(new) = l * b

= (3x/2) * (3y/4) = (9xy/8)

➻ New Area of Field = (9xy/8)

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▪Finally ,

% of change in Area = (change/original) * 100%

⇒ [(9xy/8) - xy]/xy * 100%

⇒ (xy/8)/xy * 100

⇒ (⅛) * 100%

⇒ (100/8)%

⇒ 12.5%

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❖ % of change in Area of Rectangular Field = 12.5%

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