Difference between Lengths of 2 Sides of a Triangle

Q. Question 6
The lengths of two sides of a triangle are 12 cm and 15 cm. Between what two values should the length of the third side fall?

Q.

If two sides of a triangle are 4 cm and 5 cm then which of the following cannot be the length of third side?

1. 10 cm

2. 7 cm

3. 6 cm

4. 8 cm

Q. If the length of two sides of a triangle are 5 cm and 12 cm, then which of the following cannot be the length of the third side?

1. 9 cm
2. 5 cm
3. 13 cm
4. 12 cm

Q.

Two sides of a triangle have lengths of 5 units and 6 units respectively. Which of the following is a possible length for the third side?

1. 11

2. 12

3. 13

4. 10

Q.

Question 1 (ii)
Is it possible to have a triangle with the following sides?
3 cm, 6 cm, 7cm

Q.

Which of the following statements are not correct?

a) The sum of any two sides of a triangle is greater than the third side.
b) A triangle can have all its angles acute.
c) A right-angled triangle cannot be equilateral.
d) The difference of any two sides of a triangle is greater than the third side.

Q.

Each of the 2 side of isosceles triangle os three times as large as third side . If the perimeter of the triangle is 28 cm, find each of the the triangle

Q.

State True or False whether a triangle with sides 2 cm, 3 cm and 5 cm is possible.

1. True

2. False

Q. The two sides of a triangle are 5 cm and 12 cm. Which of the following can be the third side of the triangle?

1. 5 cm
2. 10 cm
3. 13 cm
4. 4cm

Q. $A$ and $B$ can do a piece of work in $45$ days and $40$ days respectively. They begin together but $A$ leaves after some days and $B$ completes the rest in $23$ days. For how many days did $A$ work ?

1. $9$ days
2. $6$ days
3. $8$ days
4. $12$ days

Q.

A triangle with sides 2 cm, 3 cm and 5 cm is possible.
True or false?

1. True

2. False

Q.

A triangle with sides 2cm, 3cm and 5cm is possible.

1. True

2. False

Q. Find the area of the shaded portion in the following figure :

Q.

Sum of any two sides of a triangle is always _________ than the third side.

1. Equal

2. Not sure

3. Lesser

4. Greater

Q.

Question 72

State whether the statement is True or False.

The difference between the lengths of any two sides of a triangle is smaller than the length of third side.

Q. The hypotenuse of a triangle is 2.5 cm. If one of the sides is 1.5 cm, find the length of the other side.

Q. If the area of a triangle is $1176{cm}^2$ and base: corresponding altitude is $3:4$, then the altitude of the triangle is:

1. $42cm$
2. $52cm$
3. $54cm$
4. $56cm$

Q.

Which of the following sides can give a valid triangle?

1. 12 cm, 3 cm, 7 cm

2. 2 cm, 3 cm, 7 cm

3. 5 cm, 3 cm, 7 cm

4. 2 cm, 10 cm, 7 cm

Q. In a $\Delta$ABC, which of the given condition holds?

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

Q.

What could be the length of the third side of a triangle whose other two sides are 3 cm and 8 cm?

1. True

2. False

3. 13
4. 15

Q. The triangle ABC formed by $AB=5cm,BC=8cm,AC=4cm$ is

1. an isosceles triangle only
2. a scalene triangle only
3. an isosceles right triangle
4. scalene as well as a right triangle

Q.

Which of the following sides form a triangle?

1. 5.2 cm, 1.1 cm, 2.5 cm

2. 10.5 cm, 4.5 cm, 4.5 cm

3. 7.2 cm, 4.1 cm, 3.5 cm

4. 7.2 cm, 4.1 cm, 2.5 cm

Q. Which of the following can be the third side of the triangle when two sides are 10 cm, 5 cm?

1. 7 cm
2. 2 cm
3. 1 cm
4. 4 cm

Q. The difference between the lengths of any two sides of a triangle is lesser than the length of the third side.

1. False
2. True

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. The two sides of a triangle are 5cm and 12cm. Which of the following can be the third side of the triangle?

1. 5cm
2. 10cm
3. 13cm
4. 4cm

Q. Which of the following can be the third side of the triangle when two sides are 10cm, 5cm?

1. 7cm
2. 2cm
3. 1cm
4. 4cm

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. If two sides of an isosceles $\Delta$ are $3$ cm and $8$ cm, then the length of the third side is :

1. $3$ cm
2. $8$ cm
3. none
4. $3$ cm or $8$ cm

Q. $\Delta$ABC is isosceles with AB$=$AC$=7.5$cm and BC$=9$cm. The height AD from A to BC, is $6$cm. Find the area of $\Delta$ABC. What will be the height from C to AB i.e., CE?