21. A triangle ABC with AB = 3 cm, BC = 6 cm
and AC = 4 cm is enlarged to A DEF such
that the longest side of A DEF = 9 cm. Find
the scale factor and hence, the lengths of the
other sides of A DEF.
Answers
Answered by
9
SOLUTION
Triangle ABC is enlarged to DEF. So, the two triangles will be similar.
∴
A
B
D
E
=
B
C
E
F
=
A
C
D
F
∴ABDE=BCEF=ACDF
Longest side in ΔABC = BC = 6 cm
Corresponding longest side in ΔDEF = EF = 9 cm
Scale factor =
E
F
B
C
=
9
6
=
3
2
=
1.5
EFBC=96=32=1.5
∴
A
B
D
E
=
B
C
E
F
=
A
C
D
F
=
2
3
∴ABDE=BCEF=ACDF=23
D
E
=
3
2
(
A
B
)
=
9
2
=
4.5
cm
DE=32(AB)=92=4.5 cm
D
F
=
3
2
A
C
=
12
2
=
6
cm
DF=32AC=122=6 cm
Answered by
2
Answer:
Step-by-step explanation:
Largest side of ABC is BC = 6
BC is enlarged to 9
So scale factor = 9/6 = 1.5
Other sides will be 3*1.5 = 4.5 and 4*1.5 = 6.
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