Question

What is an inequality to represent the perimeter of a triangle if two sides measure 3 meters and 8 meters

Answer 1

16 m < P < 19 m

Explanation:

we know that

The Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

Let

x----> the length of the third side

Applying the triangle inequality theorem

1) 3+8 > c

11 > c

c < 11 m

2) c+3 > 8

c> 5 m

so

the measure of the third side must be

5 m < c < 8 m

therefore

The perimeter of the triangle is equal to

P=3+8+c

P=11+c

The inequality is equal to

(11+5) m < P < (11+8) m

16 m < P < 19 m