Question

Following are some measurements of sides,Check whether they can form a triangle .
a) 6,8,12
b) 5,9,3
c) 11,6,6
d) 80,15,60
e) 8,6,10
f) 6,6,6
Give the step by step explanation please yaar it is urgent

Answer 1

Steps to check whether they can form a triangle :

• Use triangle inequality theorm :

• Add the two smaller measurements of sides.

• According to triangle inequality theorm, The sum of the two smaller sides is greater than the third side.

• If the sum of the smaller sides is not greater then the third side it cannot form a triangle.

• If the sum of the smaller sides is greater then the third side it can form a triangle.

• Then, We will get our answer.

Let's do the given questions now -

a) 6,8,12

b) 5,9,3

c) 11,6,6

d) 80,15,60

e) 8,6,10

f) 6,6,6

Now, As we see -

a) 6,8,12

• Here, The smaller sides are - 6 & 8

$\implies \sf 6 + 8$

$\implies \sf 14$

$\sf \implies12 < 14$

∴ Hence, 6,8,12 will form a triangle.

b) 5,9,3

• Here, The smaller sides are - 5 & 3.

$\implies \sf 5 + 3$

$\implies \sf 8$

$\sf \implies 9 > 8$

∴ Hence, 5,9,3 will not form a triangle.

c) 11,6,6

• Here, The smaller sides are - 6 & 6.

$\implies \sf 6 + 6$

$\implies \sf 12$

$\sf \implies11< 12$

∴ Hence, 11,6,6 will form a triangle.

d) 80,15,60

• Here, The smaller sides are - 15 & 60.

$\implies \sf 15 + 60$

$\implies \sf 75$

$\implies \sf 80 > 75$

∴ Hence, 80,15,60 will not form a triangle.

e) 8,6,10

• Here, The smaller sides are - 6 & 8.

$\implies \sf 6 + 8$

$\implies \sf 14$

$\implies \sf 10 < 14$

∴ Hence, 8,6,10 will form a triangle.

f) 6,6,6

• Here, The smaller sides are - 6 & 6.

$\implies \sf 6 + 6$

$\implies \sf 12$

$\implies \sf 6 < 12$

∴ Hence, 6,6,6 will form a triangle.