Question

5) The length and the breadth of a rectangle are 25 cm and 15 cm, respectively. If the length is increased by 12% and the breadth is decreased by 20%, what will be the percentage increase decrease in the area of the rectangle?​

Answer 1

Given that:

• The length and the breadth of a rectangle are 25 cm and 15 cm, respectively.
• The length is increased by 12% and the breadth is decreased by 20%.

To Find:

• What will be the percentage increase or decrease in the area of the rectangle?

We have:

• Length = 25 cm
• Breadth = 15 cm

We know that:

Area of a rectangle = Length × Breadth

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ = 25 × 15

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ = 375

ㅤ∴ ㅤActual area = 375 cm²

When length is increased by 12%.

New length = 25 × (100 + 12)% cm

ㅤㅤㅤㅤㅤㅤ= 25 × 112% cm

ㅤㅤㅤㅤㅤㅤ= 25 × 1.12 cm

ㅤㅤㅤㅤㅤㅤ= 28 cm

When breadth is decreased by 20%.

New breadth = 15 × (100 - 20)% cm

ㅤㅤㅤㅤㅤㅤㅤ= 15 × 80% cm

ㅤㅤㅤㅤㅤㅤㅤ= 15 × 0.8 cm

ㅤㅤㅤㅤㅤㅤㅤ= 12 cm

Finding the new area:

New area = New length × New breadth

ㅤㅤㅤㅤㅤ= 28 × 12

ㅤㅤㅤㅤㅤ= 336

ㅤ∴ ㅤNew area = 336 cm²

Here we get:

• New area is less than the actual area. Thus, there is a decrease in the area of the rectangle.

Finding the percentage decrease:

Percentage decrease = {(Actual area - New area) × 100}/(Actual Area)

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ= {(375 - 336) × 100}/375

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ= {39 × 100}/375

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ= 10.4

Hence,

• The percentage decrease in the area of the rectangle is 10.4.

Answer 2

Refer the given attachment