Question

In two or more complete sentences, explain the theorem used in solving for the range of possible lengths of the third side, AB of ABC

(they said the right angle was wrong since it doesnt have a right angle square)​

Answer 1

Triangle Inequality Theorem

see the explanation

Explanation:

see the attached figure to better understand the problem

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

In the triangle ABC of the figure

Applying the Triangle Inequality Theorem

1) First case

`10+8 > x`

solve for x

Combine like terms left side

`18 > x`

Rewrite

`x < 18\ units`

2) Second case

`8+x > 10`

solve for x

subtract 8 both sides

`x > 10-8`

`x > 2\ units`

therefore

The range of possible lengths of the third side AB is the interval (2,18)

All real numbers greater than 2 units and less than 18 units