Question

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

Answer 1

Answer:

56 triangle in the shape

Answer 2

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

Solution :-

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
• 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 3 triangles with sides as (6,2,7) , (6,3,6) and (6,4,5) can be draw with other two sides as natural numbers .

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