Sum of the Lengths of 2 Sides of a Triangle

Q.

The sum of any two sides of a triangle is always less than the third side. Say true or false.

1. True

2. False

Q.

The length of two sides of a triangle are $7cm$ and $9cm$. The length of the third side may lie between

a) $1cm$ and $10cm$
b) $2cm$ and $8cm$
c) $2cm$ and $16cm$
d) $1cm$ and $16cm$

Q.

Question 1 (i)
Is it possible to have a triangle with the following sides?
2 cm, 3 cm, 5cm

Q.

Question 1 (iii)
Is it possible to have a triangle with the following sides?
6 cm, 3 cm, 2cm

Q.

Question 138

Check whether the following measures (in cm) can be the sides of a right-angled triangle or not.
1.5, 3.6, 3.9

Q.

Take any point $O$ in the interior of a triangle $PQR$.

Is

$\left(i\right)OP+OQ>PQ$?

$\left(ii\right)OQ+OR>QR$?

$\left(iii\right)OR+OP>RP$?

Q.

Question 31

Which of the following can be the length of the third side of a triangle whose two sides measure 18 cm and 14 cm?

a) 4 cm
b) 3 cm
c) 5 cm
d) 32 m

Q.

Which of the following could represent the sides of a triangle?

1. 3, 4, 5

2. 1, 2, 3

3. 2, 4, 6

4. All of these

Q. Which of the following combination of sides (in cm) helps to construct a triangle?

1. 4, 4, 8
2. 7, 8, 9
3. 2, 4, 8
4. 3, 6, 9

Q. Which of the following combination of sides (in cm) helps to construct a triangle?

1. 2, 4, 8
2. 4, 4, 8
3. 7, 8, 9
4. 3, 6, 9

Q.

Question 3
AM is a median of a triangle ABC. Is AB + BC + CA > 2AM? (Consider the sides of triangles ABM and AMC.)

Q.

Question 74

State whether the statement is True or False.

Sum of any two angles of a triangle is always greater than the third angle.

Q.

Question 1

Four options are given, out of which only one is correct. Choose the correct one.

The sides of a triangle have lengths (in cm) 10, 6.5 and a, where a is a whole number. The minimum value that a can take is

(a) 6
(b) 5
(c) 3
(d) 4

Q.

Question 10

In $\Delta ABC$,

a) AB + BC > AC
b) AB + BC < AC
c) AB + AC < BC
d) AC + BC < AB

Q.

Question 35

If the length of two sides of a triangle are 6 cm and 10 cm, then the length of the third side can be

a) 3 cm
b) 4 cm
c) 2 cm
d) 6 cm

Q.

Which of the following could represent length of sides of a triangle?

1. 2, 4, 6

2. All of these

3. 3, 4, 5

4. 1, 2, 3

Q.

The lengths of two sides of a triangle are $12cm$ and $15cm$. Between what two measures should the length of the third side fall?

Q.

Fill the circles on the sides of the given triangle with so as to get the sum on each side as .

Q.

Question 2 (ii)
Take any point O in the interior of a triangle PQR:
Is OQ + OR > QR?

Q.

The three sides of a triangle are 3 cm, 4 cm and 5 cm. What type of triangle is this?

Q.

Question 71

State whether the statement is True or False.

Sum of two sides of a triangle is greater than or equal to the third side.

Q.

Given is an isosceles triangle ABC. The length of one of its sides is represented by $s$. The other two sides are of equal length. Their length is two times the length of the side represented by $s$. Express the perimeter of the triangle in terms of $s$.

Q.

In a$△ABC$, $AD$is median. Show that $AB+BC+AC>2AD$

Q.

Is it possible to have a triangle with the following sides?

(i) 2 cm, 3 cm, 5 cm (ii) 3 cm, 6 cm, 7 cm

(iii) 6 cm, 3 cm, 2 cm

Q. Two sides of a triangle are 5 cm and 9 cm long. What can be the length of its third side?

Q. Is it possible to draw a triangle, the lengths of whose sides are given below?

(i) 1 cm, 1 cm, 1 cm
(ii) 2 cm, 3 cm, 4 cm
(iii) 7 cm, 8 cm, 15 cm
(iv) 3.4 cm, 2.1 cm, 5.3 cm
(v) 6 cm, 7 cm, 14 cm

Q.

Sum of lengths of any two sides of a triangle is always equal to the third side.

1. True

2. False

Q.

Can a triangle have three sides whose lengths are

$3.4cm,4.7cm,6.2cm?$

Q. Fill in the blanks:

(i) A right triangle cannot have an ...... angle.
(ii) The acute angles of a right triangle are ...... .
(iii) Each acute angle of an isosceles right triangle measures ...... .
(iv) Each angle of an equilateral triangle measures ...... .
(v) The side opposite the right angle of a right triangle is called ...... .
(vi) The sum of the lengths of the sides of a triangle is called its...... .

Q. The sides of a triangle have lengths (in cm) $10,6.5$ and $a$, where $a$ is a whole number. What is the minimum value that $a$ can take?