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

1. True

2. False

Q.

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

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. 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

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