Question

Kevin has three pieces of wood. Board A is 5 inches long, board B is 7 inches long, and board C is 13 inches long. If the full length of each board is used, can the three pieces of wood be placed together to form a triangle?

Answer 1

Answer:

The three pieces of wood when placed together cannot form a triangle when used for full length.

Step-by-step explanation:

Given:

Length of Board A = 5 inches

Length of Board B = 7 inches

Length of Board C = 13 inches

We need to find whether three pieces of wood be placed together to form a triangle.

Solution:

Now we know that;

By Triangle inequality property:

"A triangle can be form when sum of the length of the 2 side of triangle is greater than third."

For this all three condition must be fulfilled.

We will check for each condition whether it is true or not.

Condition 1: Board A + Board B > Board C

$5+7>13\\\\12>13$

Which is false.

Condition 2: Board B + Board C > Board A

$7+13>5\\\\20>5$

Which is true.

Condition 3: Board C + Board A > Board B

$13+5>7\\\\18>5$

Which is true.

From above we can see that 2 conditions are true and 1 is false and for triangle creation all 3 conditions must be true.

Hence The three pieces of wood cannot be placed together to form a triangle when used for full length.