Question

How much area does it occupy?
length ofa rectangular field is increased by 50% and its breadth is decreased by 50% to forma new rectangular field. What will be the change in the area of the new field?​

Answer 1

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the length of rectangle be a

And width of rectangle be b

Area = ab

Now,

New length = a + 50% of a

= a+ 50a/100

= a+a/2

= 3a/2

New width = b - 50% of b

= b - b/2

= b/2

New Area = 3a/2 * b/2

= 3ab/4

Decrease in Area = ab - 3ab/4

= ab/4

% of Decrease in Area = [(ab/4) * 100] / ab

= 100 / 4

= 25 %

Answer 2

Answer:

$area \: of \: reactangle \: = lb$

Suppose length = l

Breadth =b

$according \: to \: question \: \\ length \: is \: increased \: by \: 50\% \\ so \\ new \: length \: = l - \frac{50l}{100} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{50l}{100} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{l}{2}$

$now \: breadth \: is \: decreased \: by \: 50\% \\ so \\ new \: breadth \: = b + \frac{50b}{100} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{3 {b} }{2}$

New area of the reactangle =lb

$area \: of \: reactangle \: = \frac{3b}{2} \times \frac{l}{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{3lb}{4}$

Here,

Area of new reactangle is less than old reactangle

So, total area decrease =

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

$deacrease \: area \: in \: percent \: \\ = \: \frac{ \frac{lb}{4} }{lb} \times 100 \\ \\ = 25\%$

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