two sides of a rectangle are 20cm and 10cm. They are increased in the ratio 2:3 and 3:7. Find the percentage increased in its area?
To find the percentage increase in the area of the rectangle, we need to compare the original area with the increased area.
1. Calculate the original area of the rectangle:
Original Area = Length x Width
Original Area = 20 cm x 10 cm
Original Area = 200 cm²
2. Calculate the increased length and width based on the given ratios:
Ratio 1 = 2:3
Increased Length (Ratio 1) = Original Length x 2/3
= 20 cm x 2/3
= 40/3 cm
Increased Width (Ratio 1) = Original Width x 2/3
= 10 cm x 2/3
= 20/3 cm
Ratio 2 = 3:7
Increased Length (Ratio 2) = Original Length x 3/7
= 20 cm x 3/7
= 60/7 cm
Increased Width (Ratio 2) = Original Width x 3/7
= 10 cm x 3/7
= 30/7 cm
3. Calculate the increased areas using the increased length and width values:
Increased Area (Ratio 1) = Increased Length (Ratio 1) x Increased Width (Ratio 1)
= (40/3 cm) x (20/3 cm)
= 800/9 cm²
Increased Area (Ratio 2) = Increased Length (Ratio 2) x Increased Width (Ratio 2)
= (60/7 cm) x (30/7 cm)
= 1800/49 cm²
4. Calculate the percentage increase in the area for each ratio:
Percentage Increase (Ratio 1) = (Increased Area (Ratio 1) - Original Area) / Original Area x 100
= (800/9 cm² - 200 cm²) / 200 cm² x 100
= (800/9 cm² - 900/9 cm²) / 200 cm² x 100
= -100/9 cm² / 200 cm² x 100
= -100/1800 x 100
≈ -5.56%
Percentage Increase (Ratio 2) = (Increased Area (Ratio 2) - Original Area) / Original Area x 100
= (1800/49 cm² - 200 cm²) / 200 cm² x 100
= (1800/49 cm² - 9800/49 cm²) / 200 cm² x 100
= -8000/4900 cm² / 200 cm² x 100
= -8000/980000 x 100
≈ -0.82%
Therefore, the percentage increase in the area of the rectangle for Ratio 1 is approximately -5.56% and for Ratio 2 is approximately -0.82%. Note that the negative sign indicates a decrease in area.
To find the percentage increase in the area of the rectangle, we need to calculate the initial and final areas and then compute the percentage increase.
Let's start by finding the initial area of the rectangle.
Initial sides of the rectangle:
Length = 20 cm
Width = 10 cm
Initial area = Length * Width = 20 cm * 10 cm = 200 cm²
Now, let's calculate the final areas based on the two given ratios.
For the ratio 2:3:
Final length = Initial length * 2 = 20 cm * 2 = 40 cm
Final width = Initial width * 3 = 10 cm * 3 = 30 cm
Final area (ratio 2:3) = Final length * Final width = 40 cm * 30 cm = 1200 cm²
For the ratio 3:7:
Final length = Initial length * 3 = 20 cm * 3 = 60 cm
Final width = Initial width * 7 = 10 cm * 7 = 70 cm
Final area (ratio 3:7) = Final length * Final width = 60 cm * 70 cm = 4200 cm²
Now, we can calculate the percentage increase in the area using the following formula:
Percentage increase = ((Final Area - Initial Area) / Initial Area) * 100
For ratio 2:3:
Percentage increase (ratio 2:3) = ((1200 cm² - 200 cm²) / 200 cm²) * 100 = 500%
For ratio 3:7:
Percentage increase (ratio 3:7) = ((4200 cm² - 200 cm²) / 200 cm²) * 100 = 2000%
Therefore, the area of the rectangle increased by 500% when the sides were increased in the ratio 2:3 and by 2000% when increased in the ratio 3:7.
herefore, new area of rectangle = xy
Original area = 20 × 10 = 200 cm2
Therefore, increase in area of rectangle = new area of rectangle - original area = 700 cm2 - 200 cm2 = 500 cm2
Now, percentage increase in area
the way I understand the wording .....
new length/20 = 3/2
new length = 30
new width/10 = 7/3
new width = 70/3
new area = 30(70/3) = 700
old area = 20(10) = 200
increase = 500
percentage increase = 500/200 * 100% = 250%