the length of a rectangle is halved, while its breadth is tripled. what is the percentage change in area
What is the percentage change in the area of a rectangle if its length is halved while its breadth is tripled?
Answer:
To determine the percentage change in the area of a rectangle when its length is halved and its breadth is tripled, we will follow these steps:
Step 1: Understand the Original Area
Let’s define:
- Original Length of the rectangle as ( L )
- Original Breadth of the rectangle as ( B )
The original area (( A_{\text{original}} )) can be calculated using the formula for the area of a rectangle:
A_{\text{original}} = L \times B
Step 2: Calculate the New Dimensions and Area
With the modifications:
- The new Length becomes ( \frac{L}{2} )
- The new Breadth becomes ( 3B )
The new area (( A_{\text{new}} )) can be calculated as follows:
A_{\text{new}} = \left(\frac{L}{2}\right) \times (3B)
Simplifying this expression:
A_{\text{new}} = \frac{3}{2} \times L \times B
Step 3: Determine the Percentage Change in Area
To find the percentage change in area, we use the formula for percentage change:
\text{Percentage Change} = \left(\frac{A_{\text{new}} - A_{\text{original}}}{A_{\text{original}}}\right) \times 100\%
Substituting the values of ( A_{\text{new}} ) and ( A_{\text{original}} ):
\text{Percentage Change} = \left(\frac{\frac{3}{2} \times L \times B - L \times B}{L \times B}\right) \times 100\%
Simplify the expression:
\text{Percentage Change} = \left(\frac{\frac{3}{2} - 1}{1}\right) \times 100\%
\text{Percentage Change} = \frac{1}{2} \times 100\%
\text{Percentage Change} = 50\%
Final Answer:
The percentage change in the area of a rectangle, when its length is halved and its breadth is tripled, is an increase of 50%.