A rectangle has dimensions 40m × 25m. If the length and breadth are increased by 15% find the percentage increases in its area.

The area of the rectangle can be obtained by multiplying its length and breadth.

Answer: The percentage increase in the area of the rectangle is 32.25%.

Let's find first the area of the given rectangle then the percentage increase in its area.

Explanation:

Let's draw a diagram of the rectangle.

The rectangle has dimensions 40 m × 25 m.

AB = 40 cm and BC = 25cm

Area of the given rectangle = Length × Breadth

= AB × BC

= 40 × 25 = 1000 m²

Let's draw a diagram of the rectangle if the length and the breadth are increased by15%.

Now, the new dimensions of the rectangle would be,

New length, A'B' = 40 + (40 × 15/100) = 40 + 6 = 46 m

New breadth, B'C' = 25 + (25 × 15/100) = 25 + 3.75 = 28.75 m

Now, Area of this given rectangle = New Length × New Breadth

= A'B' × B'C'

= 46 × 28.75 = 1322.5 m²

Now, percentage increase in the area of the rectangle = (Change in Area / Initial Area) × 100%

= [(1322.50 - 1000) / 1000 × 100]%

= [322.50/1000 × 100]%

= 32.25%

Thus, the percentage increase in the area of the rectangle is 32.25%.