A student construted a triangle ABC with sides AB=5cm, BC=6.5cm and AC=7cm
and then constructed a AADE similar to AABC such that each of its sides are
5
of the corresponding sides of AABC.The length of AD and AE obtained by
calculation are respectively equal to
E
A
7cm and 9.8cm
B
B. 3.4cm and 6.5cm
6.5cm
5cm
C. 6.5cm and 9.8cm
7cm
D. 10cm and 11.5cm
Α1 Α2
A3
A4 A5
A6
AT
Answers
Given :- A student constructed a triangle ABC with sides AB = 5cm, BC=6.5cm and AC = 7cm . And then constructed a ∆ADE similar to ∆ABC such that each of its sides are (5/7) of the corresponding sides of ∆ABC. The length of AD and AE obtained by calculation are respectively equal to ?
Solution :-
we know that, when two triangles are similar ,
- Ratio of their corresponding sides are equal .
so, ∆ADE ~ ∆ABC { given) .
then,
→ AD/AB = DE/BC = AE/AC = 5/7 (given)
therefore,
→ AD/5 = 5/7
→ AD = (25/7) cm .
and,
→ AE/7 = (5/7)
→ AE = 5 cm .
Note :- if sides are given as (7/5) then one of given options will match.
then,
→ AD/AB = DE/BC = AE/AC = 7/5 (given)
therefore,
→ AD/5 = 7/5
→ AD = 7 cm .
and,
→ AE/7 = (7/5)
→ AE = 49/5 = 9.8 cm .
Hence, The length of AD and AE obtained by calculation are respectively equal to
Option (A) 7cm and 9.8cm .
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Answer:
A student construted a triangle ABC with sides AB=5cm, BC=6.5cm and AC=7cm
and then constructed a AADE similar to AABC such that each of its sides are
5
of the corresponding sides of AABC.The length of AD and AE obtained by
calculation are respectively equal to
E
A
7cm and 9.8cm
B
B. 3.4cm and 6.5cm
6.5cm
5cm
C. 6.5cm and 9.8cm
7cm
D. 10cm and 11.5cm
Α1 Α2
A3
A4 A5
A6
AT