Question

the length of a rectangular fields ifs increased by 50 percent and its breadth is decreased by 50 percent to form a new rectangular field.Find the percentage change in the area of the fields

Answer 1

decreased by 25%
150*50= 7500 original 10000

Answer 2

Answer:

Let the original length be 'l' and the breadth be 'b'.

Hence the Area of the rectangular field originally is:

→ Area = lb

Now it is given that the length is increased by 50% and the breadth is decreased by 50%.

Hence the new length and breadth are given as:

$\implies l_{new} = l + \text{50 percent of l}\\\\\\\implies l_{new} = l + \dfrac{50\:l}{100}\\\\\\\implies l_{new} = l + \dfrac{l}{2} = \dfrac{3l}{2}$

Hence the new length is 1.5 l.

$\implies b_{new} = b - \text{50 percent of b}\\\\\\\implies b_{new} = b - \dfrac{50\:b}{100}\\\\\\\implies b_{new} = b - \dfrac{b}{2} = \dfrac{b}{2}$

Hence the new breadth is 0.5 b.

Calculating the new area we get:

⇒ New Area = New L × New B

⇒ New Area = 1.5 l × 0.5 b

⇒ New Area = 0.75 lb

Hence the change in the Area is given as:

⇒ Change = Old Area - New Area

⇒ Change = lb - 0.75 lb

⇒ Change = 0.25 lb

Percentage change in area is given as:

$\implies Change \:\% = \dfrac{\text{Change in Area}}{\text{Old Area}}\times 100\\\\\\\implies Change \:\% = \dfrac{0.25\:lb}{lb} \times 100\\\\\\\implies Change \:\% = 0.25 \times 100 = \boxed{ \bf{25 \:\%}}$

Hence the percentage change in area of the fields is 25%.