Question

How many triangles can be
drawn with one side 6cm and
perimeter 15 cm with other two
sides as natural no numbers?

Can anyone pls answer me with a photo??​

Answer 1

Answer:

Step-by-step explanation:

6cm,8cm,1cm

6cm,7cm,2cm

6cm,6cm,3cm

6cm,5cm,4cm

It means we can make 4 triangles whose one side is 6cm and perimeter is 15cm.

Answer 2

Answer:

3 Triangles

Step-by-step explanation:

Given:

• One side of a triangle = 6cm
• Other two sides are natural numbers.
• Perimeter = 15cm

To Find:

• Number of triangle drawn with one side 6cm & perimeter 15cm

Solution:

Let the sum of other two sides be x .

$\red{\sf{Sum\:of\:all\: sides \: of \: a\:triangle = Perimeter }}$

=> x + 6 = 15

=> x = 15 - 6

x = 9

● Therefore, Sum of other two numbers is 9 & both numbers are natural numbers.

Now, the values for other sides :-

(8 & 1) [8+1 =9]

(7 & 2) [7+2 = 9]

(6 & 3) [6+3 = 9]

(5 & 4) [5+4 = 9]

But, we know that,

$\pink{\sf{The \: \purple{sum} \: of \: any \: \purple{two \: sides} \: of \: a \: triangle }} \\ \pink {\sf{{\: is \: always \: \purple{greater} \: than \: the \: \purple{third \: side}. \: \: \: }}}$

$\sf{Measurement \: of \: sides \: of : - } \\ \sf{ \: {1}^{st} \: triangle = 8, 1 , 6} \\ \mathrm{(1 + 6) \: \red{ \bold{\cancel \green{>}}} \: 8 } \\ \mathrm{ \therefore \: It \: is \: not \: possible.} \\ \\ \sf{{2}^{nd} \: triangle = 7, 2 , 6} \\ \mathrm{(2 + 6) \green {\bold{>} }7} \\ \mathrm{\therefore \: It \: is \: possible.} \\ \\ \sf{ {3}^{rd}triangle{} = 6, 3, 6} \\ \mathrm{(3 + 6) \green{ >} 6} \\ \mathrm{{\therefore \: It \: is \: possible.}} \\ \\ \sf{ {4}^{th} triangle = 5,4,6} \\ \mathrm{{(4 + 5) \green{ >} 6}} \\ \mathrm{{{\therefore \: It \: is \: possible.}}}$

Therefore, 3 triangles can be drawn with one side 6cm & perimeter 15cm.