Inequality Property of Triangles

Q. Difference of two sides of a triangle is always _______ than the third side.

1. Greater
2. Lesser
3. Equal
4. Not sure

Q.

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. The lengths of two sides of a triangle are $16\mathrm{ft}$ and $21\mathrm{ft}$. Find the possible lengths of the third side?

Q. The length of 2 sides of a triangle 5 centimetres and 7 cm. If the third side is an integer , what is the least possible perimeter of the triangle?
A) 17 cm
B) 12 cm
C) 14 cm
D) 15 cm

Q. Two sides of a triangle are 10 cm and 7 cm. Which of the following length can be the length of the third side?

1. 17 cm
2. 16.9 cm
3. 17.2 cm
4. 17.1 cm

Q. Which of the following can be the sides of a triangle?

1. 4 cm , 5 cm , 10 cm
2. 6 cm , 12 cm , 7 cm
3. 4 cm , 4 cm , 8 cm
4. 5 cm , 3 cm , 9 cm

Q. The lengths of the three sides of a triangle are represented by three consecutive odd numbers.If the length the shortest side is represented by q, what is the length of the other two sides of the triangle??

Q.

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

1. $3cm$

2. $4cm$

3. $2cm$

4. $6cm$

Q. Two sides of an isosceles triangle ABC measure 10 cm and 18 cm. Which of the following could be the measure of the third side?

1. 18 cm
2. 10 cm
3. 20 cm
4. 15 cm

Q.

The length of two sides of a triangle are $13cm$ and $18cm$. Between what two measures should the length of the third side fall?

Q.

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

1. True

2. False

Q. In triangle ABC, AB = 15.5 cm and BC = 7.5 cm.
Then ___ < AC < ____.

1. 8, 23
2. 9, 31
3. 9, 23
4. 15, 24

Q. The length of two sides of an isosceles triangle are 9 cm and 20 cm. What is the perimeter of the triangle?

1. 49 cm
2. 27 cm
3. 60 cm
4. 38 cm

Q.

Which of the following can be the third side of the triangle when the other two sides are 9 cm, 4 cm?

1. Both A & B

2. 09:00

3. 06:15

4. 03:45

Q. In triangle ABC, AB = 15.5 cm and BC = 7.5 cm.
Then ___ < AC < ____.

1. 8, 23
2. 15, 31
3. 9, 24
4. 7, 22

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

1. 7 cm
2. 2cm
3. 6 cm
4. 5 cm

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. Lengths of two sides of a triangle are 12 cm and 15 cm. Then the length of the third side must be .

1. > 5 cm & < 27 cm
2. > 3 cm & < 27 cm
3. > 5 cm & < 12 cm

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 sum of lengths of any two sides of a triangle is equal to the length of the third side.

1. True
2. False

Q.

Two sides of a scalene triangle measure 7 cm and 3 cm. What could be the measure of the third side?

1. 9 cm
2. 10 cm
3. 12 cm
4. 11 cm

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. The square of the hypotenuse of an isosceles right angle triangle is 72 sq. cm. What is the length of each side?

Q.

Which of the following correctly indicates whether a triangle can have sides with lengths $3.5,5.3$ and $16.5$, and also provides the correct explanation?

1. No; $3.5+16.5$ is greater than $5.3$

2. Yes; $3.5+5.3$ is greater than $16.5$

3. No; $3.5+5.3$ is less than $16.5$

4. Yes; $16.5+5.3$ is greater than $3.5$

Q. The _____ of any two sides of a triangle is greater than the third side.

1. sum
2. difference
3. product
4. sum of the product

Q. In a triangle, the side opposite to the greater angle will be greater than the side opposite to the smaller angle.

1. True
2. False

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