Question

James has three iron rods. Rod A is 3 feet long, rod B is 8 feet long, and rod C is 13 feet long. If the full length of each rod is used, can the three iron rods be placed together to form a triangle?

Answer 1

Answer:

The three iron rods cannot be placed together to form a triangle.

Step-by-step explanation:

We have been given that James has three iron rods. Rod A is 3 feet long, rod B is 8 feet long, and rod C is 13 feet long. We are asked to determine whether the lengths of all rods can be used to form a triangle.

We will use triangle inequality theorem to solve our given problem.

Triangle inequality theorem states that sum of two sides of a triangle must be greater than 3rd side.

Using triangle inequality theorem, we will get inequalities as:

$13+3>8...(1)$

$16>8...(1)$

$3+8>13...(2)$

$11>13....(2)$

We can see that our 2nd inequality is not true because 11 is not greater than 13.

Since sum of two sides is not greater than 3rd side, therefore, the three iron rods cannot be placed together to form a triangle.