If the length and breadth of a rectangular plot are increased by 50% and 20%…

Concept

When two perpendicular dimensions are scaled, the area scale factor is the product of the two linear scale factors.

A percentage increase of p% changes a dimension by the factor (1 + p/100).

Application

1. Let the original length be L and breadth be B, so the original area is LB.

2. A 50% increase changes the length to 1.5L, and a 20% increase changes the breadth to 1.2B.

3. The new area is (1.5L)(1.2B) = 1.8LB. Therefore, the area multiplier is 1.8 = 9/5 = 1 4/5.

Cross-check

1. Start with a 10 by 10 plot, whose original area is 10 × 10 = 100.

2. After the increases, the dimensions become 15 by 12.

3. The new area is 15 × 12 = 180.

4. The ratio 180/100 = 1.8 = 1 4/5 independently confirms the area multiplier.

Result

Thus, the area becomes 1 4/5 times the original area.