Sum of the lengths of any two sides of a triangle is greater than the length of the ____.a)first sideb)second sidec)third sided)none of theseCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

We have Triangle Inequality Theorem which states that the sum of any 2 sides of a triangle must be greater than the measure of the third side. This means that as you know the two sides greater than the third, you know what all sides will not make a triangle.

Answer

Hi friend ,here is your answerNo! it's not necessa

ry. The sum of any 2 angles of a triangle, may be greater or shorter than

Answer

Explanation:
In a triangle, the sum of the lengths of any two sides is always greater than the length of the third side. This is known as the Triangle Inequality Theorem.

Triangle Inequality Theorem:
The Triangle Inequality Theorem states that for any triangle with sides of lengths a, b, and c, the following inequality holds true:
a + b > c
b + c > a
a + c > b

Proof:
To understand why this theorem is true, let's consider a simple example.
Suppose we have a triangle with sides of lengths 3, 4, and 5. We can test the theorem by substituting the values into the inequality:
3 + 4 > 5
7 > 5
This inequality is true, so the theorem holds for this example.

General Case:
Now let's consider the general case. Suppose we have a triangle with sides of lengths a, b, and c. We can assume without loss of generality that a ≤ b ≤ c.
To prove the Triangle Inequality Theorem, we need to show that:
a + b > c
b + c > a
a + c > b

1. a + b > c:
We can assume a ≤ b ≤ c. Since c is the longest side, a + b < 2c.='' therefore,='' a='' +='' b='' /> c.

2. b + c > a:
Since a ≤ b ≤ c, a + b < 2c.='' therefore,='' b='' +='' c='' /> a.

3. a + c > b:
Since a ≤ b ≤ c, a + b < 2c.='' therefore,='' a='' +='' c='' /> b.

Conclusion:
Therefore, the sum of the lengths of any two sides of a triangle is always greater than the length of the third side. Thus, the correct answer is option 'C', which is the third side.

Answer

C

Answer

Fertails are rich in potasium nitrogen and phosphorus. True and false

Answer

Thirth

Answer

Third side

Answer

Hello

i asmita

the answer is third side
by

Answer

Third

Similar Class 7 Doubts

The length of that hypotenuse of a right triangles is 13cm.lf one of that side of the triangle be 5 cm long,find the length of the other side. Related: Sum of the Lengths of Two Sides of a Triangle: Triangle Inequality Theorem?

What is answer of this question. The length of two sides of a triangle are 4cm and 6cm.Between what two measures should the length of the third side fall ?

If lenghts of two sides of a triangle are 12 cm and 15 cm. between what two measures to the length of the third side shouild fall?

If we are given length of two sides of triangle and are asked to find the third how will Triangle in equality theorem state that difference between the two sides length will be the lowest value?

Top Courses for Class 7View all

Science Class 7

Mathematics (Maths) Class 7

Social Studies (SST) Class 7

English Grammar Class 7

Worksheets with solutions for Class 7

Top Courses for Class 7

Top Courses for Class 7

Related Content

Class 7 Study Material

Class 7 Subjects

Competitive Examinations for Class 7

NCERT Books

Reference Books for Class 7

NCERT Solutions

Other Popular Exams

Company