Relationship between Sides of a Triangle

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

1. The sum of the lengths of two sides in a triangle is always less than the length of third side.
2. The sum of the lengths of two sides in a triangle is more than the length of third side but not always.
3. The sum of the lengths of two sides in a triangle is always more than the length of third side.
4. 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?

1. AB + BC + CA = 2AM

2. AB + BC + CA $>$​ 2AM

3. AB + BC + CA $<$​ 2AM

4. AB + BC + CA = AM

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

1. 2 cm, 3 cm, 5 cm
2. 3 cm, 4 cm, 5 cm
3. 3 cm, 4 cm, 8 cm
4. 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?

1. 20, 21, 19
2. 11, 10, 22
3. 35, 96 , 61
4. 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.

1. 3 cm, 6 cm and 3 cm
2. 10 cm, 20 cm and 30 cm
3. 20 cm, 5 cm and 40 cm
4. 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. $1$

2. $4$

3. $6$

4. $7$

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 sides is always than/to the third side is a condition to construct a triangle.

1. two
2. lesser
3. greater
4. any two
5. equal

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

1. True
2. False

Q.

The third side of a triangle must be ___ than the difference between the other two sides.

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?

1. 3 cm, 4 cm, 7 cm
   
2. 2 cm, 3 cm, 7 cm
   
3. 3 cm, 4 cm, 5 cm
4. 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?

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

Q.

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

1. PQ + PR < QS

2. PQ + PR > QS

3. PQ + TR > QS

4. PQ + TR < QS

Q.

$\text{ABC is a triangle such that AB = 10 cm}\text{and AC = 3 cm. Which of the following}\text{statements are true?}$

1. $BC>7cm$

2. $BC=6cm$

3. $BC<13cm$

4. $BC=14cm$

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

1. 20, 21, 19
2. 11, 10, 22
3. 35, 96 , 61
4. 25, 2 , 22

Q. If D is any point on the side BC of $\Delta ABC$, then

1. AB + BC + CA = 2AD
2. AB + BC + CA > 2AD
3. AB + BC + CA < 2AD
4. AB + BC - CA > 2AD

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

1. less than
2. greater than
3. equal to
4. none of these