5) The rectangle is the product of a reduction with scale factor of 1 / 3 and whose missing sides are x = 1, y = 2 and z = 1.
6) The triangle is the product of an enlargement with scale factor of 2 and whose missing sides are m = 16 and n = 20.
What the values of the missing lengths in dilated triangles?
In this problem we have two cases of dilation, that is, generating new triangles by multiplying each side by the same factor. Dilations are examples of rigid transformations, that is, transformations done on geometric loci such that Euclidean distance is conserved.
Mathematically speaking, dillation can be represented by the following expression:
d = r' / r (1)
Where:
- d - Dilation factor
- r - Original length
- r' - Resulting length
Now we proceed to find the missing sides:
Rectangle 5
d = 2 / 6
d = 1 / 3 (Reduction)
Then, the missing lengths are:
x = (1 / 3) · 3 = 1
y = (1 / 3) · 6 = 2
z = (1 / 3) · 3 = 1
Triangle 6
d = 14 / 7
d = 2 (Enlargement)
Then, the missing lengths are:
m = 2 · 8 = 16
n = 2 · 10 = 20
To learn more on dilations: https://brainly.com/question/13176891
#SPJ1
