Question

the length of a rectangle field in is increased by 50% and its breadth is decreased by 50% to find a new rectangular field find the perimeter change in the area of the field

Answer:- let length and breadth of the rect field are X cm and Y CM

It's area =XY cm^2
Increased length =X+50x/100=X+X/2=3x/2cm
decreased breadth =y-50y/100=y/2cm
Area=3x/2×y/2 = 3xy/4cm^2
Area decreased area= xy- 3 xy/4=xy
Decreased℅=xy/4×100/xy
=25℅

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Answer 1

Answer:

Solution

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Let the length of rectangle be a

And width of rectangle be b

Area =ab

Now,

New length =a+50 % of a

=a+

100

50a

=a+

2

a

=

2

3a

New width =b−50% of b

=b−

2

b

=

2

b

New Area =

2

3a

×

2

b

=

4

3ab

Decrease in Area =ab−

4

3ab

=

4

ab

% of Decrease in Area =[

4

ab

×100]/ab

=

4

100

= 25 %

Answer 2

Let the length of rectangle be a

And width of rectangle be b

Area =ab

Now,

New length = a+50% of a

$= a + \frac{50a}{100}$

$= a + \frac{a}{2}$

$= \frac{3a}{2}$

New width = b- 50% of b

$= b - \frac{50b}{100}$

$= b - \frac{b}{2}$

$= \frac{b}{2}$

New Area =

$\frac{3a}{2} \times \frac{b}{2}$

$= \frac{3ab}{4}$

Decrease in Area =

$ab - \frac{3ab}{4} = \frac{ab}{4}$

% of Decrease in Area =

$( \frac{ab}{4} \times 100) \div ab \: = \frac{100}{4}$

= 25%

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