Two sides of rectangle are 20 cm &10 cm. They are increased in ratio 2:3 & 3:7 . Find the percentage increase in its area?
20*10 = 200
20*3/2 * 10*7/3 = 200 *7/2 = 700
increase = 500
500/200 = 2.5
2.5 * 100 = 250 %
To find the percentage increase in the area of a rectangle, we need to compare the original area to the increased area.
The original area of the rectangle can be calculated by multiplying the length and width:
Area = Length * Width
Given:
Length of the rectangle = 20 cm
Width of the rectangle = 10 cm
Original Area = 20 cm * 10 cm = 200 cm²
Next, we need to find the increased dimensions of the rectangle.
First ratio: 2:3
Second ratio: 3:7
To find the increased length:
Increase = 2/3 * 20 cm = 40/3 cm (rounded to two decimal places)
To find the increased width:
Increase = 3/7 * 10 cm = 30/7 cm (rounded to two decimal places)
Increased length ≈ 13.33 cm
Increased width ≈ 4.29 cm
Now, calculate the new area:
Increased Area ≈ 13.33 cm * 4.29 cm ≈ 57.14 cm² (rounded to two decimal places)
To find the percentage increase in the area:
Percentage Increase = (Increased Area - Original Area) / Original Area * 100%
Percentage Increase = (57.14 cm² - 200 cm²) / 200 cm² * 100%
Percentage Increase ≈ (-71.43%) ≈ -71.43% (rounded to two decimal places)
Therefore, the percentage increase in the area of the rectangle is approximately -71.43%.