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sydneyyyy7014
12.07.2019 •
Mathematics
Triangles def and hjk are similar. def has side lengths = 4, = 6, = 8. which of the following could be the side lengths of hjk? a.2, 6, 7 b. 8, 12, 16 c. 5, 7, 9 d. 2, 5, 7
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Ответ:
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.
Ответ:
its not 100 points only 15
Step-by-step explanation: