The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?

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Let's start with the basics of rectangle area calculation. The area of a rectangle is calculated by multiplying its length by its breadth. We have a problem where a rectangle's length is halved while its breadth is tripled. We need to find the percentage change in area. Let's represent the original rectangle with length L and breadth B, giving us an area of L times B. Now let's visualize the transformation. We start with an original rectangle having length L and breadth B. After the transformation, the new rectangle has length L divided by 2, which means the length is halved, and breadth 3B, which means the breadth is tripled. Notice how the new rectangle becomes narrower but much taller compared to the original rectangle. Let's calculate the areas step by step. The original area is L times B, which equals LB. For the new rectangle, the area is L over 2 times 3B. Simplifying this, we get L times 3B over 2, which equals 3LB over 2. This shows us that the new area is three-halves times the original area. In other words, the new area is 1.5 times larger than the original area. Now let's apply the percentage change formula. The percentage change equals new value minus original value, divided by original value, times 100 percent. Substituting our area values, we get A2 minus A1 divided by A1 times 100 percent. This becomes 3LB over 2 minus LB, all divided by LB, times 100 percent. Simplifying the numerator, we get 3LB minus 2LB over 2, which equals LB over 2. So our expression becomes LB over 2 divided by LB times 100 percent. Let's complete the final calculation. LB over 2 divided by LB equals one-half, and one-half times 100 percent equals 50 percent. Let's verify this with a numerical example. If we have an original rectangle of 4 by 6 with area 24, the new rectangle becomes 2 by 18 with area 36. The percentage change is 36 minus 24, divided by 24, times 100 percent, which equals 50 percent. Therefore, the answer is that the area increases by 50 percent when the length is halved and the breadth is tripled.