Jeremy enlarged a picture.The length of the original picture is 8cm and the width is 5cm.The length of the enlarged picture is 10cm and the width is 7cm.
A.What percent is the 10cm length of 8cm length?
B.What is the area of each picture?By what percet is the area changed?
Pls show the solution..
increase in the length from 8 to 10 is 2cm
percent increase = 2/8 = 25%
old area = 40
new area = 70
increase = 30
percent increase = 30/40 = 75%
did you realize that the increase will result in a distortion ?
The percentage increase of the length is NOT the same as the percentage increase in the width
A. To find the percentage, divide the length of the enlarged picture (10cm) by the length of the original picture (8cm), and then multiply by 100.
Percentage = (Enlarged Length / Original Length) * 100
Percentage = (10cm / 8cm) * 100
Percentage = 1.25 * 100
Percentage = 125%
So, the 10cm length is 125% of the 8cm length.
B. To find the area of each picture, multiply the length by the width.
Original Picture Area = Length * Width
Original Picture Area = 8cm * 5cm
Original Picture Area = 40cm²
Enlarged Picture Area = Length * Width
Enlarged Picture Area = 10cm * 7cm
Enlarged Picture Area = 70cm²
To find the percentage change in the area, divide the difference between the enlarged and original picture areas by the original picture area, and then multiply by 100.
Percentage Change in Area = ((Enlarged Area - Original Area) / Original Area) * 100
Percentage Change in Area = ((70cm² - 40cm²) / 40cm²) * 100
Percentage Change in Area = (30cm² / 40cm²) * 100
Percentage Change in Area = 0.75 * 100
Percentage Change in Area = 75%
So, the area of the enlarged picture is 75% larger than the area of the original picture.
To find the percentage increase in length, you can use the formula:
Percentage increase = ((new length - original length) / original length) * 100
For part A:
1. Substitute the given values:
New length = 10 cm
Original length = 8 cm
2. Plug these values into the formula:
Percentage increase = ((10 - 8) / 8) * 100
Percentage increase = (2 / 8) * 100
Percentage increase = 0.25 * 100
Percentage increase = 25%
Therefore, the 10 cm length is 25% greater than the 8 cm length.
To find the area of each picture, you can use the formula:
Area = length * width
For part B:
1. Substitute the given values for the original picture:
Length = 8 cm
Width = 5 cm
2. Calculate the area:
Area of the original picture = 8 cm * 5 cm
Area of the original picture = 40 cm²
3. Substitute the given values for the enlarged picture:
Length = 10 cm
Width = 7 cm
4. Calculate the area:
Area of the enlarged picture = 10 cm * 7 cm
Area of the enlarged picture = 70 cm²
To find the percentage change in the area, you can use the formula:
Percentage change = ((new area - original area) / original area) * 100
5. Plug the values into the formula:
Percentage change = ((70 - 40) / 40) * 100
Percentage change = (30 / 40) * 100
Percentage change = 0.75 * 100
Percentage change = 75%
Therefore, the area of the enlarged picture is 75% greater than the area of the original picture.