9th Class Math Chapter 13 Sides and Angles of Triangles Short Questions Answer

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9th Class Math Chapter 13 Sides and Angles of Triangles Short Questions Answer

If 13 cm, 12cm, and 5 cm are the lengths of a triangle, then verify that difference of measures of any two sides of a triangle is less than the measure of the third side.

  

Solution: 

Let the three sides be 

a = 13cm, b = 12cm, c = 5 cm 

a – b – 13 – 12 = 1 < 5 = c 

i.e. a – b < c (i) 

12 – 5 = 7 < 13

b – c < a (ii)   

13 – 5 = 8 < 12 

i.e. a – c < b (iii)

From (i), (ii) and (iii) we find that the difference of measures of any two sides of a triangle is less than the measure of the third side.

If 10cm, 6cm and 8cm are the lengths or a triangle, then verify that sum of measures of two sides of a triangle is greater than the third side.

Solution: 

Let the measure of the sides of the triangle be

a = 10 cm, b – 6 cm, c = 8cm 

10 + 6 = 16 > 8 

a + b < c (i)

6 + 8 = 14 > 10

b + c < a (ii)

8 + 10 = 18 > 6 

c + a > b (iii)

From (i), (ii) and (iii) we conclude that the sum of measures of two sides of a triangle is greater than the third side.

3cm, 4cm and 7cm are not the lengths of the triangle. Give the reason.

Solution: 

Let a = 3cm, b = 4cm, c = 7cm 

a + b = 3 + 4 = 7 = c 

i.e. a + b = c 

Since we know that for a triangle sum of measures of two sides should be greater than measure of the third side. 

3 + 4e 7 

So, 3cm, 4cm and 7cm are not the, lengths of the triangle

If 3cm and 4cm are the lengths two sides of a right-angle triangle then what should be the third length of the triangle.

 

Solution: 

Let the three sides be 

3³ + 4² = a² (Pythagoras theorem)

9 + 16 = a²

a² = 25

⟹ a = 5 

The third Length is 5 cm.

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