# Geometry Escape Challenge C just for code

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## Question:

Geometry Escape Challenge C just for code

fill in the white spaces in the table
what does the hint of the crack the code mean?

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

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

(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)

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

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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

70(3x + 1) = 80(3x – 7)

210x + 70 = 240x – 560

210x – 240x = -70 – 560

-30x = -630

x = -630/-30

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.