If two sides of a triangle are 5 cm and 1.5 cm, the length of its third side can not be......
Answers
We have,
- Lengths of two sides of a ∆ : 5 cm and 1.5 cm
And we need to determine:
- What can't be the length of the Third side?
So, Let's find:
Before solving and determining anything further, let's know the two simple inequalities of triangle.
1) The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
2) The difference of the lengths of any two sides of a triangle is always less than the length of the third side.
Then,
According to the inequality,
⍟ First side + Second side > Third side
➛ Third side < 5 cm + 1.5 cm
➛ Third side < 6.5 cm ----------(1)
And,
⍟ First side - Second side < Third side
➛ Third side > 5 cm - 1.5 cm
➛ Third side > 3.5 cm ----------(2)
Combining (1) and (2),
➛ 3.5 cm < Third side < 6.5 cm
The range of the third side is between 3.5 cm and 6.5 cm. The length of the third side can't be 3.5 cm or less than that. And neither it will be 6.5 cm or more than that.
꧁ Correct Question:- ꧂
Two sides of a triangle are of lengths 5 cm and 1.5 cm. The length of the third side of the triangle cannot be
(A) 3.6 cm
(B) 4.1 cm
(C) 3.8 cm
(D) 3.4 cm
꧁ Answer ꧂
✯ Given ✯
- Two sides of a triangle are :-
- 5 cm
- 1.5 cm
✯ To find ✯
- The length of its third side can be not from following given above options.
✯ Solution ✯
We know that, a closed figure formed by three intersecting lines (or sides) is called a triangle.
[According to the triangle inequality"The sum of the length of any sides of a triangle must be greater than or equal to the length of third side ]
If difference of two sides < third side and sum of two sides > third side.
So, Third side AC should:
AB-BC < AC < AB + BC
5-1.5 < AC < 5 + 1.5
3.5 < AC < 6.5
Hence, it cannot be 3.4 because it is less than 3.5. Option D is correct.