Question

A triangle has two sides of length 14.8 and 12.8. What compound inequality describes the possible lengths for the third side, x? Write a compound inequality like 1

Answer 1

2<x<27.6

Explanation:

Let the sides of the triangle be x, y and z. For a triangle having the three sides, the following are true:

x+y>z.... 1

x+z>y....2

y+z>x....3

Let z= 14.8 and y = 12.8

Substitute the given values into 1

x+12.8>14.8

x > 14.8-12.8

x>2

Or 2<x

Substituting into equation 3;

14.8+12.8>x

27.6>x or x<27.6

Combine both inequalities

2<x and x<27.6

We will have;

2<x<27.6

Hence the compound inequality is 2<x<27.6