a If the lengths of sides of one of the similar triangles are half the length of the sides of the other one, then the scale factor is 1:2.
B
b If the lengths of sides of one of the similar triangles are three times the length of the sides of the other one, then the scale factor is 1:3.
A
a
Area: 10 square units Ratio between the areas: 1:4
B
b
Area: 7 square units Ratio between the areas: 1:9
Practice makes perfect
a We are given that each side length of â–ł JKL is half the length of â–ł ABC. This means that the ratio between the corresponding sides of â–ł JKL and â–ł ABC is 1:2.
1/2=12a/a=12h/h
As we know that the area of a triangle is the product of its base and height multiplied by 12, we can evaluate the ratio of the areas.
12( 12a)*( 12h)/12a* h=14/1=1/4
We got that the ratio of the areas of these triangles is 1:4. Notice that this ratio is the squared ratio of corresponding side lengths. Using this ratio, we can evaluate the area of the triangle JKL. To do this, let's multiply the area of â–ł ABC, 40, by the ratio of the areas.
1/4* 40=10
The area of â–ł JKL is 10 square units.
b This time we are given that each side length of â–ł ABC is three times the length of â–ł JKL. This means that the ratio between the corresponding sides of â–ł JKL and â–ł ABC is 1: 3.
1/3=1 3a/a=1 3h/h
As we know that the area of a triangle is the product of its base and height multiplied by 12, we can evaluate the ratio of the areas.
12( 1 3a)*( 1 3h)/12a* h=19/1=1/9
We got that the ratio of the areas of these triangles is 1:9. Notice that this ratio is a squared ratio of corresponding sides. Using this ratio, we can evaluate the area of the triangle JKL. To do this, let's multiply the area of â–ł ABC, 63, by the ratio of the areas.
1/9* 63=7
The area of â–ł JKL is 7 square units.
