4) The length of three sides of 4 triangles are given below which triangles
cannot be drawn?
a) 8.6cm, 13.3cm, 4.8cm.
b)8.4cm, 13.3cm, 4.9cm.
c)8.6cm, 4.9cm, 13.2cm.
d)8.4cm, 13.2cm, 5.9cm.
Answers
Answer:
The answer is option C 8.6 cm,4.9cm,13.2cm.
Given :- The length of three sides of 4 triangles are given below which triangles cannot be drawn ?
a) 8.6cm, 13.3cm, 4.8cm.
b)8.4cm, 13.3cm, 4.9cm.
c)8.6cm, 4.9cm, 13.2cm.
d)8.4cm, 13.2cm, 5.9cm.
Solution :-
we know that,
- Sum of any two sides of a ∆ is greater than the third side .
- Difference of any two sides of a ∆ is smaller than the third side .
Checking given options we get,
a) 8.6cm, 13.3cm, 4.8cm.
- 8.6 + 4.8 = 13.4
- 13.4 > 13.3 (sum is greater than third side)
- 13.3 - 4.8 = 8.5
- 8.6 > 8.5 (3rd side is greater than difference.)
- 13.3 - 8.6 = 4.7 => 4.8 > 4.7 (3rd side is greater than difference.)
therefore, triangle with given sides can be drawn .
b)8.4cm, 13.3cm, 4.9cm.
- 8.4 + 4.9 = 13.3
- 13.3 = 13.3
- Sum is not greater than third side but equal .
therefore, triangle with given sides can not be drawn .
c)8.6cm, 4.9cm, 13.2cm.
- (8.6 + 4.9) > 13.2 . (Rest sum sides is clearly greater.)
- (13.2 - 4.9) < 8.6 .
therefore, triangle with given sides can be drawn .
d)8.4cm, 13.2cm, 5.9cm.
- (8.4 + 5.9) > 13.2 . (Rest sum sides is clearly greater.)
- (13.2 - 5.9) < 8.4 .
- (13.2 - 8.4) < 5.9 .
therefore, triangle with given sides can be drawn .
Hence, triangle with sides b)8.4cm, 13.3cm, 4.9cm cannot be drawn .
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