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