Inequalities in a Triangle

Q.

Question 2 (i)
Find the values of unknowns x and y in the following diagram:

Q.

In a $△$ABC, $\angle$ABC = ${30}^{\circ }$ and $\angle$ACB = ${45}^{\circ }$. Which is the longest side in this triangle?

1. AB
2. BC
3. CA
4. All are same in length

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 lengths of two sides of a triangle are 13cm and 16cm. The third side should lie between 'a' cm and 'b' cm for the triangle to be formed. What will be the value of a + b?

1. 26
2. 29
3. 32
4. 35

Q. The lengths of two sides of a triangle are 13cm and 16cm. The third side should lie between 'a' cm and 'b' cm for the triangle to be formed. What will be the value of a + b?

1. 26
2. 29
3. 32
4. 35

Q.

The sum of all the exterior angles of a triangle is ___ (in degrees)​.

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

1. True

2. False

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.

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

1. False

2. True

Q.

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

1. True

2. False

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. 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. In $△ABC$, if $\angle B=\angle C={45}^{\circ }$, then which of the following is/are the longest side(s)?

1. AB and BC
2. AC
3. AB
4. BC