Test: Inequalities In A Triangle

QUESTION: 1

If AB = 8 cm, BC = 15 cm and CA = 19 cm. State whether these sides form a triangle ΔABC.

A.
Yes, they form a triangle as sum of two sides is greater than the third side
B.
Yes, they form an isosceles triangle
C.
Yes, they form an right angled triangle
D.
No, a triangle cannot be formed

Solution:

QUESTION: 2

In the figure, AC > AB and D is a point on AC such that AB = AD, then

A.
BC = 1/2 AD
B.
BC > CD
C.
BC = AD
D.
BC < AD

Solution:

QUESTION: 3

Which of the following does not represent the sides of a triangle?

A.
2 cm, 3 cm, 6 cm
B.
7 cm, 5, cm, 3 cm
C.
3 cm, 2 cm, 4 cm
D.
5 cm, 8 cm, 4 cm

Solution:

QUESTION: 4

In figure, which of the following statement is true?

A.
∠B is the greatest angle in triangle
B.
∠B is the smallest angle in triangle
C.
∠A is the smallest angle in triangle
D.
∠B = ∠C

Solution: Since, angle opposite to the smallest side is the smallest angle,<b (opposite to smallest side AC = 15cm) is the smallest angle.

QUESTION: 5

In triangle ABC, ∠B = 35°, ∠C = 65° and the bisector of ∠BAC meets BC in P, choose the correct order of inequality

A.
AP >BP > CP
B.
BP >AP > CP
C.
CP >BP >AP
D.
none

Solution:

QUESTION: 6

If length of the largest side of a triangle is 12 cm then other two sides of triangle can be:

A.
4.8 cm, 8.2 cm
B.
6.4 cm, 2.8 cm
C.
7.6 cm, 3.4 cm
D.
3.2 cm, 7.8 cm

Solution:

QUESTION: 7

Two sides of triangle are of lengths 5 cm and 1.5 cm. The length of the third side of the triangle cannot be

A.
3.6 cm
B.
3.4 cm
C.
3.8 cm
D.
4.1 cm

Solution:

QUESTION: 8

In a triangle ABC this statement will always be true.

A.
AB+BC>AC
B.
AB
C.
AB+BC
D.
AB+BC=AC

Solution:

QUESTION: 9

In ΔPQR, S is any point on the side QR, then

A.
PQ + QR + RP < 2PS
B.
PQ + QR + RP = 2PS
C.
PQ + QR + RP > 2PS
D.
PQ + QR + RP < 4PS

Solution:

QUESTION: 10

In ΔABC, ∠A = 40° and ∠B = 60°. The longest side is

A.
BC
B.
AC
C.
AB
D.
CD

Solution:

QUESTION: 11

The perimeter of a triangle is…. the sum of its medians.

A.
less than
B.
greater than twice
C.
equal to
D.
greater than

Solution:

QUESTION: 12

It is not possible to construct a triangle when its sides are:

A.
3 cm, 5 cm, 5 cm
B.
6 cm, 7 cm, 10 cm
C.
8.3 cm, 3.4 cm, 6.1 cm
D.
5.4 cm, 2.2 cm, 3.1 cm

Solution:

QUESTION: 13

Which of the following is incorrect ?

A.
If two angles of a triangle are unequal, then the greater angle has the greater side opposite to it
B.
Sum of any two sides of a triangle is greater than twice the median drawn to the third side
C.
The sum of any two sides of a triangle is always greater than the third side
D.
Sum of the three sides of a triangle is less than the sum of its three medians