Question

the two sides of triangle is 3cm and 2cm respectively. the third side is ​

Answer 1

5cmm.....

We know that (3+4) cm is greater than third side.

Thus, the third side is smaller than 7 cm

(ii) we know that (4−3) cm is smaller than third side .

Thus, the third side is greater than 1cm.

Therefore, 1 cm < third side <7 cm.

Thus, 5 cm can be the length of third side for a triangle.

Answer 2

• The length of third side of given triangle must be greater than 1 cm and smaller than 5 cm .

Given :- Two sides of a triangle are 3cm and 2cm respectively.

To Find :- Length of third side ?

Concept used :-

• Sum of any two sides of a ∆ is greater than the third side .
• Difference between any two sides of a ∆ is smaller than the third side .

Solution :-

Let us assume that, the length of third side of given triangle is equal to x cm .

First case :- Sum of any two sides of a ∆ is greater than the third side .

So,

→ Two sides of given triangle are = 2 cm and 3 cm

and,

→ Third side of given triangle = x cm

then,

→ Sum of two sides > Third side

→ (2 + 3) > x

→ 5 > x .

Therefore we can conclude that , third side of given triangle is smaller than 5 cm .

Second case :- Difference between any two sides of a ∆ is smaller than the third side .

So,

→ Two sides of given triangle are = 2 cm and 3 cm

and,

→ Third side of given triangle = x cm

then,

→ Difference between of two sides < Third side

→ (3 - 2) < x

→ 1 < x .

Therefore we can conclude that , third side of given triangle is greater than 1 cm .

From both case results we can conclude that, the length of third side of given triangle must be greater than 1 cm and smaller than 5 cm .

[ Possible integer value of length of third side is equal to 2cm, 3cm or 4cm. ]

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