Answer. Option B: 8,12,16
Solution:
Like the triangles are similar, their sides must be proportional, then if:
DE=4, EF=6 and FD=8; and the proportional sides are HJ, JK and KH respectively, then:
HJ/DE=JK/EF=KH/FD
Replacing DE=4, EF=6 and FD=8 in the equation above:
HJ/4=JK/6=KH/8
In option A or D, if HJ=2 (the smaller side)
2/4=JK/6=KH/8
Simplifying the fraction
1/2=JK/6=KH/8
Using the first equality:
1/2=JK/6
Solving for JK: Multiplying both sides of the equation by 6:
6(1/2)=6(JK/6)
6/2=6 JK/6
3=JK
JK=3
Then options A (JK=6) or D (JK=5) are no possibles.
Using HJ=8 (the smaller side) in the option B:
8/4=JK/6=KH/8
2=JK/6=KH/8
Using the first equality:
2=JK/6
Solving for JK: Multiplying both sides of the equation by 6:
6(2)=6(JK/6)
12=6 JK/6
12=JK
JK=12
Using the second equality:
2=KH/8
Solving for KH: Multiplying both sides of the equation by 8:
8(2)=8(KH/8)
16=8 KH/8
16=KH
KH=16
Option B is possible.
In option C, if HJ=5 (the smaller side)
5/4=JK/6=KH/8
Using the first equality:
5/4=JK/6
Solving for JK: Multiplying both sides of the equation by 6:
6(5/4)=6(JK/6)
30/4=6 JK/6
15/2=JK
JK=15/2=7.5
Then option B (JK=7) is no possible.
