In Fig. 7, if A ABC ~ A DEF and their sides of lengths (in cm) are marked
along them, then find the lengths of sides of each triangle.
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Answered by
18
AB = 9 cm
BC = 12 cm
CA = 15 cm
DE = 18 cm
EF = 24 cm
FD = 30 cm
Step-by-step explanation:
We have Δ ABC and Δ DEF are similar.
Hence,
So,
⇒ 2x - 1 = 9
⇒ 2x = 10
⇒ x = 5
Therefore, AB = 2x - 1 = 9 cm.
BC = 2x + 2 = 12 cm.
CA = 3x = 15 cm.
DE = 18 cm.
EF = 3x + 9 = 24 cm.
And, FD = 6x = 30 cm. (Answer)
Answered by
2
We have Δ ABC and Δ DEF are similar.
Hence, \frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD}
DE
AB
=
EF
BC
=
FD
CA
So, \frac{2x - 1}{18} = \frac{3x}{6x}
18
2x−1
=
6x
3x
⇒ 2x - 1 = 9
⇒ 2x = 10
⇒ x = 5
Therefore, AB = 2x - 1 = 9 cm.
BC = 2x + 2 = 12 cm.
CA = 3x = 15 cm.
DE = 18 cm.
EF = 3x + 9 = 24 cm.
And, FD = 6x = 30 cm.
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