The sides of a rectangle are 5 cm and 10 cm.The sides are then increased by 50% each.The percentage increase in the area is %.

Step 1: Calculate the original area of the rectangle. The area of a rectangle is given by the formula length x width. So, the original area is 5 cm x 10 cm = 50 cm².

Step 2: Calculate the new dimensions of the rectangle. The sides are increased by 50%, so the new length is 5 cm + 50% of 5 cm = 7.5 cm, and the new width is 10 cm + 50% of 10 cm = 15 cm.

Step 3: Calculate the new area of the rectangle. The new area is 7.5 cm x 15 cm = 112.5 cm².

Step 4: Calculate the percentage increase in the area. The formula for percentage increase is (new value - original value) / original value x 100%. So, the percentage increase in the area is (112.5 cm² - 50 cm²) / 50 cm² x 100% = 125%.

So, the percentage increase in the area of the rectangle is 125%.