Question

How many triangles canbe drawn with one side 6cm and perimeter 15cm with other two sides as natural numbers?

Answer 1

GivEn:

• How many triangles canbe drawn with one side 6cm and perimeter 15cm with other two sides as natural numbers?

To find:

• Number of triangles can be made.

Solution:

Here,

• Perimeter = 15cm
• Side = 6cm

⠀⠀━━━━━━━━━━━━━━━━━━━⠀

« Now, Using the perimeter formula,

As we know that,

• Perimeter = Sum of all sides

→ 15 - 6

→ 9

⠀⠀━━━━━━━━━━━━━━━━━━━⠀

« Now, Finding the two triangles,

We know that,

• Sum of two sides must be greater than the greatest side.

Greatest side can be either 6 or 7,

Finding sides,

→ 6 + 2 < 7

→ 6 + 3 < 6

→ 5 + 4 < 6

∴ Hence, Three triangles can be made if one side is 6 cm & perimeter is 15 cm.

Answer 2

Given :

• How many triangles can be drawn with one side 6 cm and perimeter 15 cm .

To find :

• Triangles can be made .

Solution :

one side = 6 cm

Perimeter = 15 cm

Perimeter = sum of all three sides

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

$\sf \: 9=1+8,2+7,3+6,4 +5$

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