Question

3. The length of two sides of a triangle are 5cm and 11cm. Between what two whole numbers should lie the measure of the third side?


pls guys tell me the answer fast

Answer 1

Given :-

The length of two sides of a triangle are 5cm and 11cm.

To Find :-

Between what two whole numbers should lie the measure of the third side?

Solution :-

At first finding sum of two sides

Sum = 5 + 11 = 16

Now,

Let the third side be x

Now,

According to property of triangle

Sum of any two side is greater than 3rd side

At first

x + 5 > 11

x > 11 - 5

x > 6 (Eqⁿ 1)

Again,

5 + 11 > x

16 > x (Eqⁿ 2)

Again,

11 + x > 5

x > 5 - 11

x > -6 (Eqⁿ 3)

Thus we concluded

x lies b/w 6 to 16

Answer 2

Answer :

6 and 16

Concept to be used :

• Inequality in a triangle : The sum of any two sides of a triangle is always greater than the third side .

Solution :

• Given : To sides of a triangle are 5 cm and 11 cm .
• To find : Two whole numbers between which the third side lies .

Let the third side of the triangle be x cm .

Thus ,

The three sides of the triangle are ;

5 cm , 11 cm , x cm .

Also ,

We know that , the sum of any two sides of a triangle is always greater than the third side .

Thus ,

• 5 + 11 > x

→ 16 > x

→ x < 16 ------(1)

• 11 + x > 5

→ x > 5 - 11

→ x > -6 -------(2)

• 5 + x > 11

→ x > 11 - 5

→ x > 6 --------(3)

Now ,

From inequations (1) , (2) and (3) ;

We can conclude that ;

6 < x < 16

Thus ,

The third side of the triangle lies between the whole numbers 6 and 16 (excluding 6 and 16) .