b The area scale factor between similar figures is a square of the linear scale factor between them.
A
aPerimeter: 84 units
Area: 144 square units
B
bPerimeter: 28 units
Area: 16 square units
Practice makes perfect
a Garland tries to copy a triangle that has a perimeter of 42 units and an area of 36 square units. The zoom factor was set to 200 %, so the linear scale factor between the original triangle and a copy is 2. To find the perimeter of the resulting triangle we can multiply the perimeter by the linear scale factor.
42( 2) = 84
The resulting triangle's perimeter is 84 units. Now, let's find the area. The area scale factor between similar figures is a square of the linear scale factor between them.
(Linear scale factor)^2=( 2)^2
⇓
Area scale factor= 4
To find the area of the resulting triangle, we can multiply the original triangle's area by the area scale factor. Let's do it!
36( 4) = 144
The resulting triangle has an area of about 144 square units.
b The resulting triangle from Part A has a perimeter of 84 units and an area of 144 square units. Now the linear scale factor is 13, so to find the perimeter of the new triangle we should multiply 84 by 13. let's do it!
The new triangle's perimeter is 28 units. The area scale factor between similar figures is a square of the linear scale factor between them.
(Linear scale factor)^2=( 1/3)^2
⇓
Area scale factor= 1/9
To find the area of the new triangle, we should multiply 144, the area of a triangle from Part A, by the area scale factor of 19.
