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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?

## Answer:

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 **ratio**s 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

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.

Learn more about **similar triangles** on:

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