If a 5 by 7 picture is enlarged by 150%, what is the new area?
Scale factor with area and volume
If a figure is enlarged by a factor of five, the length will be five times greater, the width will be five times greater and the height will be five times greater.
The area will therefore be five times five times greater.
The volume will therefore be five times five times five times greater.
So:
Scale factor length = k
Scale factor area = k2
Scale factor volume = k3
Example 1
A photo with an area of 150 cm2 will be enlarged by a factor of 7.
What will be the area of the enlargement?
Answer:
The scale factor for the area will be 72.
New area = 72 × 150 = 7350 cm2.
Example 2
Exactly 27 cubes fit in a certain box.
Someone finds this box too small and orders a new box.
This new box is the old box enlarged by a factor of 2.
How many cubes will fit in the new box?
Answer:
The scale factor for the volume will be 23.
So 23 × 27 = 216 cubes will fit in the new box.
So here, areanew = 2.5*5x7=87.5
so the scale factor is sqrt(2.5)
length=7*sqrt(2.5)
height=5*sqrt(2.5)
THX
To find the new area after enlarging the picture by 150%, we need to follow these steps:
1. Start by finding the area of the original picture. The original picture is 5 by 7, so the area is calculated by multiplying the length by the width: Area = Length × Width = 5 × 7 = 35 square units.
2. Calculate the scale factor for the enlargement. The picture is enlarged by 150%, which means it is increased by 1.5 times its original size.
3. Multiply the original area by the square of the scale factor. Since the scale factor only applies to the length and width, we need to square it to account for the change in area: New Area = Original Area × (Scale Factor)^2 = 35 × (1.5)^2 = 35 × 2.25 = 78.75 square units.
Therefore, the new area of the enlarged picture is approximately 78.75 square units.