Question

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

Answer 1

Answer:

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

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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 A > 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
• 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+36,6+6 >3

• 6-36,6-6<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.