DIRECTIONS for the question: Solve the following question and mark the best possible option.
In the figure below, AB = 12 cm. D is the midpoint of BC. Also, DE ⊥ BC, BG = 5 cm and CH = 15 cm. What is the ratio of DE : GE?
A)
12 : 11
B)
11 : 9
C)
13 : 11
D)
15 : 11
E)
10 : 13
E
Using similarity in triangle ABG and ACH
AB/BG = AC/CH
12/5 = AC/15
AC = 36
BC = AC-AB = 36-12 = 24
BD = DC = 12
AG2 = AB2+BG2
AG = 13
Using similarity in ABG and ADE
AB/AG = AD/AE
12/24 = 13/AE
AE = 26
GE = AE-AG = 13
AB/BG = AD/DE
12/5 = 24/DE
DE = 10
DE:GE= 10:13
