Question

how many triangles can be draw with one side 6cm and perimeter 15cm with other two sides as natural numbers ?​

Answer 1

Given :- how many triangles can be draw with one side 6cm and perimeter 15cm with other two sides as natural numbers ?

Answer :-

Let other two sides be a and b .

so,

→ Perimeter = 15 cm

→ One side = 6 cm

→ 6 + a + b = 15

→ a + b = 15 - 6 = 9 .

now, we know that,

• sum of any two side of ∆ > Third side .
• Difference between any two sides < Third side.

then,

→ a + b > 9 and a - b < 6

checking possible values with these two conditions we get,

if a and b are 1 , 8 or 8 , 1

• 6 + 1 + 8 = 15
• 6 + 1 < 8
• Side are not possible Possible .

if a and b are 2 , 7 or 7 , 2

• 6 + 2 + 7 = 15

1. 6 + 2 > 7 , 2 + 7 > 6 , 7 + 6 > 2 .

• 6 - 2 < 7 , 7 - 2 < 6 , 7 - 6 < 2 .
• Side are Possible .

if a and b are 3 , 6 or 6 , 3

• 6 + 6 + 3 = 15
• 6 + 3 > 6 , 6 + 6 > 3
• 6 - 3 < 6 , 6 - 6 < 3
• Side are Possible .

if a and b are 4 , 5 or 5 , 4

• 4 + 5 + 6 = 15
• 4 + 5 > 6 , 5 + 6 > 4 , 4 + 6 > 5 .
• 5 - 4 < 6 , 6 - 5 < 4 , 6 - 4 < 5 .
• Side are Possible .

therefore, we can conclude that , total 6 triangles can be draw with other two sides as natural numbers .

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Answer 2

Given :  Triangles with one side 6cm and perimeter 15cm

To Find : how many triangles can be drawn with other two sides as natural number

Solution:

one side  = 6 cm

Perimeter = 15 cm

Perimeter = sum of all three sides

=> sum of other two sides = 15 - 6 = 9 cm

9 = 1 + 8  , 2 + 7  , 3 + 6 , 4  + 5

ow in a triangle sum of two sides is greater than 3rd side

6  ,  1  ,  8   Does not satisfy

Hence 3 triangles are possible

6 , 2 , 7

6 , 3 , 6

6 , 4 , 5

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