Question

choose the correct option in which a triangle cannot be constructed with the given lengths of sides.

3cm, 4cm ,5cm

7cm, 6cm, 5cm

10cm, 7cm, 2cm

12cm, 8cm ,6cm

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Answer 1

Answer:

To find which sides form a triangle than,

the sum of any two sides should be greater than the third side .

option (c) cannot be constructed

because,

10+7>2

10+2>7

but ,

7+2<10

all the three conditions should satisfy

therefore , option (c) is incorrect

Answer 2

Answer:

With 10 cm, 7 cm, 2 cm triangle cannot be constructed

Step-by-step explanation:

The given problem is about checking weather the construction of triangle is possible with the following sides

before checking that remember the following points

In a triangle the sum of the length of the two sides is greater than the length of the third side

And the difference between the two sides of a triangle is less than the length of the third side.    

Given sides 1) 3 cm, 4 cm ,5 cm ; 2)7 cm, 6 cm,  5 cm ; 3)10 cm, 7 cm, 2 cm ;  4) 12 cm, 8 cm ,6 cm

 ⇒   1)  3 cm , 4 cm, 5 cm                    

         ⇒ 3 + 4 = 7 > 5                      

         ⇒  4 $-$ 3 = 1 < 5    

         ⇒triangle can be constructed

⇒   2)  7 cm, 6 cm,  5 cm    

         ⇒ 7 + 6 = 13  > 5

         ⇒ 7 - 6  = 1 < 5  

         ⇒   triangle can be constructed

⇒  3)  10 cm, 7 cm, 2 cm        

        ⇒ 10 +7 = 17 > 2

        ⇒  10 $-$ 7 = 3 > 2

        ⇒triangle cannot be constructed

⇒ 4)  12 cm, 8 cm, 6 cm  

         ⇒  12 + 8 =20 > 6

         ⇒  12 $-$ 8 = 4 < 6  

         ⇒ triangle can be constructed