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Mathematics
Problem
Two right-angled triangles
△
A
B
C
\triangle ABC
△
A
B
C
and
△
D
E
F
\triangle DEF
△
D
E
F
satisfy
∠
B
=
90
∘
\angle B = 90^\circ
∠
B
=
9
0
∘
,
∠
E
=
90
∘
\angle E = 90^\circ
∠
E
=
9
0
∘
,
A
B
=
9
cm
AB = 9\,\text{cm}
A
B
=
9
cm
,
D
E
=
9
cm
DE = 9\,\text{cm}
D
E
=
9
cm
,
A
C
=
15
cm
AC = 15\,\text{cm}
A
C
=
15
cm
, and
D
F
=
15
cm
DF = 15\,\text{cm}
D
F
=
15
cm
. It is also given that
E
F
=
12
cm
EF = 12\,\text{cm}
E
F
=
12
cm
. a. (i) Prove that
△
A
B
C
≅
△
D
E
F
\triangle ABC \cong \triangle DEF
△
A
B
C
≅
△
D
E
F
. b. (ii) Find the length of
B
C
BC
B
C
. c. (iii) Determine the perimeter of
△
A
B
C
\triangle ABC
△
A
B
C
.
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