Question

if the length of the rectangle is increased by 10% and the breadth is reduced by 10% , then the area of the resulting rectangle ___________ than the area of the original rectangle. options 1) increases by 1% 2) reduces by 1%. 3) dose not change. 4) the answer can very.​

Answer 1

Solution :-

Let us assume that, Length and breadth of original rectangle are 10x cm and 10y cm.

so,

→ Area of rectangle = L * B = 10x * 10y = 100xy cm².

now,

→ New length = 110% of 10x = 11x cm.

→ New breadth = 90% of 10y = 9y cm.

so,

→ Area of resulting rectangle = L * B = 11x * 9y = 99xy cm².

then

→ Area of resulting rectangle decreased by = 100xy - 99xy = xy cm².

therefore,

→ Area of resulting rectangle decreased by = (xy * 100) / 100xy = 1% (Ans.) (2)

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Answer 2

Given : length of rectangle increased by 10% and breadth reduced by 10%

 Then the area of the resulting rectangle ___________ than the area of the original rectangle.

To Find : Fill in the blank

1) increases by 1%

2) reduces by 1%.

3) dose not change.

4) the answer can very.​

Solution:

Let say original rectangle  = 10L  and 10B   units

area = 10L * 10B = 100LB sq units

length of rectangle increased by 10%  = 10L + (10/100)10L  = 11L

breadth of rectangle decreased by 10%  = 10B - (10/100)10B  =9B

Area of resulting rectangle = 11L * 9B  = 99LB sq units

Decrease in area = 100LB - 99LB =  LB

% Decrease in area = (LB/100LB) * 100 = 1 %

1 % decrease in area

reduces by 1%  is correct answer.

if the length of the rectangle is increased by 10% and the breadth is reduced by 10% , then the area of the resulting rectangle reduces by 1% than the area of the original rectangle.

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