Applying the knowledge of similar triangles, the crack code is: 4,361.
What are Similar Triangles?
If two triangles are similar, therefore, their corresponding sides are proportional, which means the ratios of their corresponding sides are the same.
a. ΔDEF is similar to ΔVRT, therefore:
15/37.5 = DE/30
Cross multiply
DE = (30 × 15)/37.5
DE = 12
b. ΔPAK is similar to ΔWNK, therefore:
62.5/45 = PK/54
Cross multiply
PK = (54 × 62.5)/45
PK = 75
c. ΔSFC is similar to ΔAFY, therefore:
36/(x + 6) = (22.4 + 16)/16
36/(x + 6) = 38.4/16
Cross multiply
(36)(16) = 38.4(x + 6)
576 = 38.4x + 230.4
576 - 230.4 = 38.4x
345.6 = 38.4x
345.6/38.4 = x
x = 9
d. ΔBNV is similar to ΔHZG, therefore:
20/(x - 1) = 30/(x + 8)
Cross multiply
20(x + 8) = 30(x - 1)
20x + 160 = 30x - 30
20x - 30x = -160 - 30
-10x = -190
x = 19
e. ΔEFC is similar to ΔKLM, therefore:
(x - 5)/(5x - 1) = 12/78
Cross multiply
78(x - 5) = 12(5x - 1)
78x - 390 = 60x - 12
78x - 60x = 390 - 12
18x = 378
x = 21
FE = 5x - 1 = 5(21) - 1
FE = 104
f. ΔMRT is similar to ΔARS, therefore:
(3x + 1)/80 = (3x - 7)/70
Cross multiply
70(3x + 1) = 80(3x - 7)
210x + 70 = 240x - 560
210x - 240x = -70 - 560
-30x = -630
x = -630/-30
x = 21
MT = 3x + 1 = 3(21) + 1
MT = 64
Numbers along the bolded column = 2, 7, 9, 1, 0, 4 = 279,104
The quotient of 279,104 and 64 = 279,104/64 = 4,361.
Thus, applying the knowledge of similar triangles, the crack code is: 4,361.
Learn more about similar triangles on:
https://brainly.com/question/10251012
