Question

. The sides of a triangle (in cm) are given below: in which case
the construction of triangle is not possible?
a) 8,7,3
b) 8,6,4 c) 8,4,4 d) 7,6,5​

Answer 1

c) 8, 4, 4

Step-by-step explanation:

A triangle construction is only possible if the sum of any of its two sides is greater than the third side.

A triangle of side lengths a, b, and c can be constructed only if -

$a+b>c\\b+c>a\\a+c>b$

If all of the above inequalities are fulfilled, then only a triangle can be constructed.

Option (a):

$a=8,b=7,c=3\\8+7=15>3\\7+3=10>8\\8+3=11>7$

So, triangle can be constructed.

Option (b):

$a=8,b=6,c=4\\8+6=14>4\\6+4=10>8\\8+4=12>6$

So, triangle can be constructed.

Option (c):

$a=8,b=4,c=4\\8+4=12>4\\4+4=8=8\\8+4=12>4$

So, triangle can't be constructed because the second inequality is not true.

Option (d):

$a=7,b=6,c=5\\7+6=13>5\\6+5=11>7\\7+5=12>6$

So, triangle can be constructed.