# Relationship between Sides of a Triangle

## Trending Questions

**Q.**Which of the following statement(s) is/are not true?

- The sum of the lengths of two sides in a triangle is always less than the length of third side.
- The sum of the lengths of two sides in a triangle is more than the length of third side but not always.
- The sum of the lengths of two sides in a triangle is always more than the length of third side.
- The differnce of the lengths of two sides in a triangle is always less than the length of third side.

**Q.**

If AM is a median of triangle ABC, then which of the following relation will always hold good?

AB + BC + CA = 2AM

AB + BC + CA > 2AM

AB + BC + CA < 2AM

AB + BC + CA = AM

**Q.**Which of the following sets of sides form a triangle?

- 2 cm, 3 cm, 5 cm
- 3 cm, 4 cm, 5 cm
- 3 cm, 4 cm, 8 cm
- 1 cm, 1 cm, 2 cm

**Q.**

The length of the two sides of the triangle are $6\mathrm{cm}\text{and}10\mathrm{cm}$. Between what two whole numbers should lie the measure of the third sides?

**Q.**Which of the following triplets (in cm) can act as sides of a triangle?

- 20, 21, 19
- 11, 10, 22
- 35, 96 , 61
- 25, 2 , 22

**Q.**

The hypotenuse of a right triangle is 26 cm long. If one of the remaining two sides is 10 cm long, find the length of the other side.

**Q.**Three side lengths are given in each of the following options. Choose the one in which a unique triangle can be constructed using SSS criterion.

- 3 cm, 6 cm and 3 cm
- 10 cm, 20 cm and 30 cm
- 20 cm, 5 cm and 40 cm
- 4 cm, 21 cm and 19 cm

**Q.**

The length of two sides of a triangle is 3 cm and 4 cm. Which of the following integral values can the third side take?

1

4

6

7

**Q.**The length of one sides of a right triangle is 4.5 cm and the length of its hypotenuse is 7.5 cm. Find the length of its third side.

**Q.**The sum of any two sides of a triangle is always

(a) equal to the third side

(b) less than the third side

(c) greater than or equal to the 3rd side

(d) greater than the 3rd side

**Q.**In each of the following, there are three positive numbers. State if these numbers could possibly be the lengths of the sides of a triangle:

(i) 5, 7, 9

(ii) 2, 10, 15

(iii) 3, 4, 5

(iv) 2, 5, 7

(v) 5, 8, 20

**Q.**The sum of the lengths of

- two
- lesser
- greater
- any two
- equal

**Q.**Difference of lengths of any two sides is always greater than the third side.

- True
- False

**Q.**

The third side of a triangle must be

**Q.**Check if a triangle with sides 5 cm, 19 cm and 20 cm can be constructed.

**Q.**Which of the following set of sides are possible for a triangle?

- 3 cm, 4 cm, 7 cm

- 2 cm, 3 cm, 7 cm

- 3 cm, 4 cm, 5 cm
- 3 cm, 3 cm, 7 cm

**Q.**Draw the triangles according to the measures given below.

(1) In ∆UVW, m∠V = 55°, m∠W = 55°, l (VW) = 7 cm.

(2) In ∆ABC, l (BC) = 4.9 cm, m∠B = 63°, m∠C = 42°

(3) In ∆NQP, l (QP) = 7.1 cm, m∠Q = 32°, m∠P = 110°

**Q.**Which of the following sets of sides form a triangle?

- 2 cm, 3 cm, 5 cm
- 3 cm, 4 cm, 5 cm
- 1 cm, 1 cm, 2 cm
- 3 cm, 4 cm, 8 cm

**Q.**

ABC is a triangle such that AB = 10 cmand AC = 3 cm. Which of the followingstatements are true?

BC>7 cm

BC=6 cm

BC<13 cm

BC=14 cm

**Q.**

In Fig. T is a point on side QR of ΔPQR and S is a point such that RT = ST. Which of the following is true?

PQ + PR < QS

PQ + PR > QS

PQ + TR > QS

PQ + TR < QS

**Q.**Which of the following triplets (in cm) can act as sides of a triangle?

- 20, 21, 19
- 11, 10, 22
- 35, 96 , 61
- 25, 2 , 22

**Q.**If D is any point on the side BC of ΔABC, then

- AB + BC + CA = 2AD
- AB + BC + CA > 2AD
- AB + BC + CA < 2AD
- AB + BC - CA > 2AD

**Q.**The sum of lengths of any two sides of a triangle is always_________the third side.

- less than
- greater than
- equal to
- none of these