Question

The lengths of two sides of a triangle are 4 cm and 6cm. Between what two measures should the length of the third side fall.

Answer 1

Answer

Length of third side of triangle is between 2 cm and 10 cm

Step by step explanation

Let x be the length of third side of triangle.

case 1. let x is largest side of triangle, then

As we know, sum of two small sides > third side

4+6>x

10>x

Case.2. As 6 is larger than 4. Let 6 be the largest side of triangle, then

x+4>6

x>6-4

x>2

This means that length of third side of triangle is between 2 cm and 10 cm

Answer 2

Hey there !

Given sides of the triangle = 4 cm , 6cm.

We know that ,

The relation between the sides of the triangle is

1 . Difference of any two sides is less than third side .

2 . Sum of any two sides is greater than third side .

So , Let the third side be " m " .

From the above relationships ;

Difference relation :

6 - 4 < m

2 < m.

Sum relation :

6 + 4 > m

10 > m.

Therefore , m lies between 2 & 10 .

m = { 3 , 4 , 5 , 6 , 7 , 8 , 9 }

Hope helped !