Question

State whether following statement is true or false.

Two sides of a triangle have lengths 7 inches and 10 inches, as shown. The length of third side must be greater than 3 inches but less than 17 inches long.

• A. True
• B. False

Answer 1

The correct option is A True

By applying the triangle inequality,

$7<x+10,10<x+7$ and $x<10+7$

We solve each of these inequalities to find

$-3<x,3<x,$ and $x<17$

As x must be positive, thus, from the given inequalities third side must be greater than 3 inches but less than 17 inches long.