Question

If the length and breadth of a rectangle is increased by 25%,find the difference between the areas of the old and new rectangles.
[Hint: Ans.9LB/16Sqcm.] ??

Answer 1

When the dimensions are increased by 25%, the new dimensions will be 125% of the old dimensions.

125 % = 125 / 100 = 1.25

Old area:

A = L ∙ B

New area:

An = 1.25 L ∙ 1,25 B = 1,25² L ∙ B = 1.5625 A

An - A = 1.5625 A - A = 0.5625 A

0.5625 = 56,25 %

Area will increase by 56.25%

By the way 0,5625 = 9 / 16

Answer 2

OR

25 % = 1 / 4

When the dimensions are increased by 25% the new dimensions will be :

1 + 1 / 4 = 4 / 4 + 1 / 4 = 5 / 4 of the old dimensions.

Old area:

A = L ∙ B

New length :

Ln = 5 L / 4

New breadth:

Bn = 5 B / 4

New area:

An = Ln ∙ Bn = 5 L / 4 ∙ 5 B / 4 = 25 L ∙ B / 16

New area - old area:

An - A = 25 L∙ B / 16 - L ∙ B =

25 L∙ B / 16 L ∙ B - 16 L ∙ B / 16 = 9 L B /16

________________________________________

The result is the same as in the previous procedure.

9 L B / 16 = 0.5625 L B = 56,25 % L B

Area will increase by 9 / 16 = 56.25%
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Answer 3

My typo in last step:

Not 25 L∙ B / 16 L ∙ B - 16 L ∙ B / 16 = 9 L B /16

Correct:

25 L∙ B / 16 - 16 L ∙ B / 16 = 9 L B /16

Answer 4

or
The areas of similar figures are proportional to the squares of their corresponding sides

area of old : area of new = 1^2 : 1.25^2
= 1 : 1.5625

so .....