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%
_________________________________________

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 .....

Answer 5

[AI-generated answer — Explain Bot]

To find the difference between the areas of the old and new rectangles, we need to calculate the area of each rectangle and then subtract.

Let's first assume the original length of the rectangle is L and the original breadth is B. Therefore, the original area (A1) is given by:

A1 = L * B

If both the length and breadth are increased by 25%, the new length (L2) and new breadth (B2) are:

L2 = L + (25/100) * L = 1.25 * L
B2 = B + (25/100) * B = 1.25 * B

The new area (A2) is given by:

A2 = L2 * B2 = (1.25 * L) * (1.25 * B) = 1.5625 * L * B

Finally, the difference between the areas of the old and new rectangles is:

Difference = A2 - A1 = (1.5625 * L * B) - (L * B) = (1.5625 - 1) * L * B = 0.5625 * L * B

Now, the answer given is in the form of 9LB/16. So, let's try to simplify the expression we obtained:

0.5625 * L * B = (9/16) * L * B

Hence, the difference between the areas of the old and new rectangles is 9LB/16 square units.