How many triangles can be drawn with one side 6 cm perimeter 15 cm with other two sides as natural number ?
Answers
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:
only three triangles are possible, and the dimensions are :
( 5 , 4 , 6 )
(6 , 3 , 6 )
(7 , 2 , 6 )
Given:
Length of one side of triangle = 6 cm
Perimeter of the triangle = 15 cm
To Find :
find the number of triangles that can be made from the given information.
Step-by-step explanation:
Side of the triangle = 6 cm
Perimeter of the triangle = 15 cm
So the sum of other two sides = Perimeter of the triangle - Side of the triangle
= 15 - 6
= 9 cm
Let the a = 6 cm
and b+ c = 9 cm
For making a triangle , essential condition is that sum of two sides is always greater than the third side.
so the pair of side can be made from the sum = 9 are
(8+1) , (7+2) , (6+3) , (5+4)
If we take :
(8 + 1) :
6 + 1 <8
So this option is not posible.
(7+2):
2+6>7
6+7>2
7+2>6
Hence this option is possible
(6+3):
6+6>6
3+6>6
Hence this option is possible
(5+4):
5+6>4
4+6>5
5+4>6
Hence this option option is also possible .
Hence only three triangles are possible, and the dimensions are :
( 5 , 4 , 6 )
(6 , 3 , 6 )
(7 , 2 , 6 )