Sum of the lengths of two sides of a triangle - class-IX

Question 1 Multiple Choice (Single Answer)

In any triangle, the side opposite to the larger (greater) angle is longer

True
False

Question 2 Multiple Choice (Single Answer)

For a triangle $ABC$, the true statement is:

${ AC }^{ 2 }={ AB }^{ 2 }+{ BC }^{ 2 }$
$AC=AB+BC$
$AC>AB+BC$
$AC<\,AB+BC$

Question 3 Multiple Choice (Single Answer)

Two sides of a triangle are of lengths 5 cm and 1.5 cm, then the length of the third side of the triangle cannot be

$\displaystyle3.6\,cm$
$\displaystyle4.1\, cm$
$\displaystyle3.8\, cm$
$\displaystyle3.4\, cm$

Question 4 Multiple Choice (Single Answer)

Which of the following sets of side lengths form a triangle?

4 m, 3 m, 11 m
7 mm, 4 mm, 4 mm
3 cm, 1.23 cm, 5 cm
3 m, 10 m, 8 m

Question 5 Multiple Choice (Single Answer)

Which is the smallest side in the following triangle?
$\displaystyle \angle P:\angle Q:\angle R=1:2:3$

$PQ$
$QR$
$PR$
cannot be determined

Question 6 Multiple Choice (Single Answer)

It is not possible to construct a triangle with which of the following sides?

$8.3\ cm, 3.4\ cm, 6.1\ cm$
$5.4\ cm, 2.3\ cm, 3.1\ cm$
$6\ cm, 7\ cm, 10\ cm$
$3\ cm, 5\ cm, 5\ cm$

Question 7 Multiple Choice (Single Answer)

The sides of a triangle (in cm) are given below:

In which case, the construction of $\triangle $ is not possible?

8, 7, 3
8, 6, 4
8, 4, 4
7, 6, 5

Question 8 Multiple Choice (Single Answer)

In $\Delta PQR, \angle P = 60^{\circ}$ and $\angle Q = 50^{\circ}$. Which side of the triangle is the longest ?

PQ
QR
PR
None

Question 9 Multiple Choice (Single Answer)

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

8.3 cm, 3.4 cm, 6.1 cm
5.4 cm, 2.3 cm, 3.1 cm
6 cm, 7 cm, 10 cm
3 cm, 5 cm, 5 cm

Question 10 Multiple Choice (Single Answer)

In $\Delta ABC, \angle B = 30^{\circ}, \angle C = 80^{\circ}$ and $\angle A = 70^{\circ}$ then,

$AB > BC < AC$
$AB < BC > AC$
$AB > BC > AC$
$AB < BC < AC$

Question 11 Multiple Choice (Single Answer)

In $\Delta ABC$, if $\angle A = 50^{\circ}$ and $\angle B = 60^{\circ}$, then the greatest side is :

AB
BC
AC
Cannot say

Question 12 Multiple Choice (Single Answer)

In $\Delta ABC$, if $\angle A = 35^{\circ}$ and $\angle B = 65^{\circ}$, then the longest side of the triangle is :

AC
AB
BC
None of these

Question 13 Multiple Choice (Single Answer)

In $\Delta ABC$, if AB $>$ BC then :

$\angle C < \angle A$
$\angle C = \angle A$
$\angle C > \angle A$
$\angle A = \angle B$

Question 14 Multiple Choice (Single Answer)

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

4.8 cm, 8.2 cm
3.2 cm, 7.8 cm
6.4 cm, 2.8 cm
7.6 cm, 3.4 cm

Question 15 Multiple Choice (Single Answer)

In $\Delta ABC, \angle A=100^{\circ}, \angle B=30^{\circ}$ and $\angle C= 50^{\circ}$,then

$AB>AC$
$AB=AC$
$AB<AC$
None of these

Question 16 Multiple Choice (Single Answer)

Out of isosceles triangles with sides of 7 cm and a base with the length expressed by whole number, the triangle with the greatest perimeter was selected. This perimeter is equal to.......

14 cm
15 cm
21 cm
27 cm

Question 17 Multiple Choice (Single Answer)

If a $\triangle PQR$ is constructed taking QR = $5$ cm, PQ = $3$ cm and PR = $4$ cm, then the correct order of the angles of the triangle is:

$\displaystyle \angle P$ < $\displaystyle \angle Q$ < $\displaystyle \angle R$
$\displaystyle \angle P$ > $\displaystyle \angle Q$ < $\displaystyle \angle R$
$\displaystyle \angle P$ > $\displaystyle \angle Q$ >$\displaystyle \angle R$
$\displaystyle \angle P$ < $\displaystyle \angle Q$>$\displaystyle \angle R$

Question 18 Multiple Choice (Single Answer)

If a triangle $PQR$ has been constructed taking $QR = 6 $ cm, $PQ = 3 $ cm and $PR = 4 $ cm, then the correct order of the angle of triangle is

$\displaystyle \angle P< \angle Q< \angle R $
$\displaystyle \angle P> \angle Q< \angle R $
$\displaystyle \angle P> \angle Q> \angle R $
$\displaystyle \angle P< \angle Q> \angle R $

Question 19 Multiple Choice (Single Answer)

The number of triangles with any three of the length $1, 4, 6$ and $8 $ cm as sides is:

$4$
$2$
$1$
$0$

Question 20 Multiple Choice (Single Answer)

Which of the following sets of side lengths will not form a triangle?

$11$ cm, $10$ cm, $11$ cm
$3$ m, $3$ m , $3$ m
$9$ mm, $9$ mm, $12$ mm
$3$ cm, $4$ cm, $7$ cm

Question 21 Multiple Choice (Single Answer)

Which is the greatest side in the following triangle?
$\displaystyle \angle A:\angle B:\angle C=4:5:6$

$AB$
$BC$
$AC$
Cannot be determined

Question 22 Multiple Choice (Single Answer)

The length of two sides of a triangle are $20 $ mm and $29 $ mm. Which of the following can be the value of third side to form the triangle?

$6 $ mm
$7 $ mm
$23 $ mm
$8 $ mm

Question 23 Multiple Choice (Single Answer)

The lengths of two sides of a triangle are $7 $ cm and $10 $ cm. What is the possible value range of the third side?

$3 $ cm $<$ third side $< 10 $ cm
$7 $ cm $<$ third side $< 10 $ cm
$3 $ cm $<$ third side $< 17 $ cm
$7 $ cm $<$ third side

Question 24 Multiple Choice (Single Answer)

The lengths of two sides of a triangle are $3 $ cm and $4 $ cm. Which of the following, can be the length of third side to form a triangle?

$0.5 $ cm
$5 $ cm
$8 $ cm
$10$ cm

Question 25 Multiple Choice (Single Answer)

Find all possible lengths of the third side, if sides of a triangle have $3$ and $9$.

$6 < x < 12$
$5 < x < 12$
$6 < x < 10$
$6 < x < 11$

Question 26 Multiple Choice (Single Answer)

The construction of a triangle $ABC$, given that $BC =$ $6$ cm, $B =$ $45 ^{\circ}$ is not possible when difference of $AB$ and $AC$ is equal to:

$6.9$ cm
$5.2$ cm
$5.0$ cm
$4.0$ cm

Question 27 Multiple Choice (Single Answer)

Find all possible lengths of the third side, if sides of a triangle have $2$ and $5$.

$2 < x < 7$
$3 > x < 7$
$3 < x > 7$
$3 < x < 7$

Question 28 Multiple Choice (Single Answer)

A triangle has side lengths of $6$ inches and $9$ inches. If the third side is an integer, calculate the minimum possible perimeter of the triangle (in inches).

$4$
$15$
$8$
$19$
$29$

Question 29 Multiple Choice (Single Answer)

Which statement is true about the difference of any two sides of a triangle?

It is greater than the third side
It is zero
It is lesser than the third side
It is lesser than zero

Question 30 Multiple Choice (Single Answer)

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

True
False

Sum of the lengths of two sides of a triangle - class-IX

Questions