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?

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

Which is false.

Condition 2: Board B + Board C > Board A

Which is true.

Condition 3: Board C + Board A > Board B

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.

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2