Question

which of the following set of lengths can be the sides of a triangle? explain why?
a) 2cm,4cm,1.9cm
b)5.5cm,6.5cm,8.9cm
c)1.6cm,3.7cm,5.3cm

the answer is b) but can you pls explain me.​

Answer 1

Step-by-step explanation:

it is a property of triangle that sum of two sides is greater than length of remaining side.

a)2+1.9 is less than 4

b)each case is right

c)1.6+3.7 is equal to 5.3 but not greater.

Answer 2

The set of lengths 5.5cm,6.5cm,8.9cm can be the sides of triangle.

Option (b) is correct.

Given:

• a) 2cm,4cm,1.9cm
• b)5.5cm,6.5cm,8.9cm
• c)1.6cm,3.7cm,5.3cm

To find:

• Which of the given set of lengths can be the sides of a triangle?
• Explain why?

Solution:

Concept to be used:

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

b)5.5cm,6.5cm,8.9cm

Ans: This set of lengths can be the sides of a triangle.

Because

5.5+6.5= 12 > 8.9

5.5+8.9 = 14.4 > 6.5

6.5+8.9= 15.4 > 5.5

Thus, all these lengths hold the property of sides of triangle.

Thus,

Triangle construction can be done.

Option b is correct.

a) 2cm,4cm,1.9cm

Ans: This set of lengths can not be the sides of a triangle.

Because

2+4= 6 > 1.9

2+1.9 = 3.9 < 4

4+1.9= 5.9> 2

Thus, all these lengths can't hold the property of sides of triangle.

Thus,

Triangle construction cannot be done.

Option a is incorrect.

c)1.6cm,3.7cm,5.3cm

Ans: This set of lengths can not be the sides of a triangle.

Because

1.6+3.7= 5.3 = 5.3

1.6+5.3 = 6.9>3.7

3.7+5.3= 9> 1.6

Thus, all these lengths can't hold the property of sides of triangle.

Thus,

Triangle construction cannot be done.

Option c is incorrect.

Thus,

The set of lengths 5.5cm,6.5cm,8.9cm can be the sides of triangle.

Option (b) is correct.

Learn more:

1) Construct triangle PQR in which PQ + PR = 6.5 cm QR = 5.4 cm, ∠Q = 40°

https://brainly.in/question/7392040

2) If the construction of a triangle abc in which ab = 6 cm, ∠a = 70° and ∠b = 40° is possible then find the measure of ∠c....

https://brainly.in/question/16013191