Tag: sum of the lengths of two sides of a triangle

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Questions Related to sum of the lengths of two sides of a triangle

Multiple choice maths triangle inequality construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle

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

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A greater angle of a angle is opposite a greater side$.$ Let $ABC$ be a triangle in which angle $ABC$ is greater than angle $BCA;$ then side $AC$ is also greater than side $AB.$ For if it is no greater$,$ then $AC$ is either equal to $AB$ or less$.$

Hence$,$ option $(A)$ is always true$.$

Multiple choice maths triangle inequality construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle

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

  1. $\displaystyle3.6\,cm$
  2. $\displaystyle4.1\, cm$
  3. $\displaystyle3.8\, cm$
  4. $\displaystyle3.4\, cm$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In a triangle, the difference between two sides should be less than the third side.
Hence,option D is correct $3.4\ cm$

Multiple choice maths triangle inequality construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle

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

  1. 4 m, 3 m, 11 m

  2. 7 mm, 4 mm, 4 mm

  3. 3 cm, 1.23 cm, 5 cm

  4. 3 m, 10 m, 8 m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A triangle can be formed only if sum of any two sides is greater than the third side.

In option $C$ sum of any two sides taken a time is greater than the third side.
$7+4>4$
$4+4>7$
$4+7>4$
So option $C$ is correct.

Multiple choice maths triangle inequality construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle

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

  1. $PQ$
  2. $QR$
  3. $PR$

  4. cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given, $\angle P: \angle Q: \angle R=1:2:3$

By applying relationship between sides and angles of a triangle, if two sides of a triangle are unequal, the side opposite to smaller angle is smaller.
Since, $\angle P$ is smallest, so $QR$ is smallest.

Multiple choice maths triangle inequality construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle

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

  1. $8.3\ cm, 3.4\ cm, 6.1\ cm$
  2. $5.4\ cm, 2.3\ cm, 3.1\ cm$
  3. $6\ cm, 7\ cm, 10\ cm$
  4. $3\ cm, 5\ cm, 5\ cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A triangle can be formed only if sum of any two sides is greater than the third side.

In option $C$
$2.3cm+3.1cm=5.4cm$
which is equal to the third side.
So a triangle can not be constructed.

Multiple choice maths triangle inequality construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle

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

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

  1. 8, 7, 3

  2. 8, 6, 4

  3. 8, 4, 4

  4. 7, 6, 5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A triangle can be formed if the sum of any two sides of triangle is greater then the third side

In option $C$ , sum of two sides is equal to third side.
So triangle can not be formed.
Option $C$ is correct.

Multiple choice maths triangle inequality construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle

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

  1. PQ

  2. QR

  3. PR

  4. None
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using angle sum property of triangle 

$\angle P+\angle Q+\angle R={ 180 }^{ \circ  }\ \Rightarrow { 60 }^{ \circ  }+{ 50 }^{ \circ  }+\angle R={ 180 }^{ \circ  }\ \Rightarrow \angle R={ 180 }^{ \circ  }-{ 110 }^{ \circ  }={ 70 }^{ \circ  }$

So $\angle R$ is the largest angle and side opposite to largest angle is the longest side.
$\therefore PQ$ is the longest side.

Multiple choice maths triangle inequality construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle

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

  1. 8.3 cm, 3.4 cm, 6.1 cm

  2. 5.4 cm, 2.3 cm, 3.1 cm

  3. 6 cm, 7 cm, 10 cm

  4. 3 cm, 5 cm, 5 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For forming a triangle sum of any two sides must be greater than the third side.

In option $B$
$2.3cm+3.1cm=5.4cm$
which is equal to the third side.
So a triangle can not be formed.
Option $B$ is correct.

Multiple choice maths triangle inequality construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle

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

  1. $AB > BC < AC$
  2. $AB < BC > AC$
  3. $AB > BC > AC$
  4. $AB < BC < AC$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In any triangle side opposite to the largest angle is the longest side.

Here $\angle C$ is largest and side opposite to it is $AB$
$\therefore AB$ is the longest side.
Then comes  $\angle A$ and side opposite to it is $BC$.
$\therefore BC$ is second longest.
Then comes $\angle B$ and side opposite to it is $AC$
So it is the smallest side.
So the decreasing order of sides is 
$AB>BC>AC$