Question

If the length of rec. is increased by 37whole 1/2% and its breadth is decreased by 20%.find %change in area​

Answer 1

Answer:-

Let us assume that the length and breadth of the rectangle are L units and B units.

We know that,

Area of a rectangle = length * breadth

Hence,

The area of the rectangle = LB unit² -- equation (1)

We have to find:

% change in the area if length is increased by 37.5 % and breadth is decreased by 20%.

New length of the rectangle = l * (100 + 37.5) / 100

→ New length of the rectangle = 137.5L/ 100 units.

New breadth of the rectangle = B * (100 - 20) / 100

→ New breadth of the rectangle = 80B/100 units.

Now,

→ Original Area of the rectangle * (100 + x) / 100 = New area of the rectangle.

Hence,

→ LB * (100 + x) / 100 = [ (137.5L) / 100 ] * [ 80B/100 ]

→ LB * [ 100 / 137.5L ] * [ 100 / 80B ] = 100 / (100 + x)

→ 10000 / 11000 = 100 / (100 + x)

→ 10 / 11 = 100 / (100 + x)

→ 10 (100 + x) = 1100

→ 100 + x = 1100/10

→ 100 + x = 110

→ x = 110 - 100

→ x = 10 %

Therefore, the area of the rectangle increases by 10% if the length is increased by 37.5% and breadth is decreased by 20%.