Question

steven is cutting an 11 ft piece of lumber into three pieces to build a triangular garden. which diagram shows a way in which he can cut the wood to create three pieces that can form a triangle? 2 ft 2 ft 7 ft 1 ft 4 ft 6 ft 3 ft 2 ft 6 ft 3 ft 4 ft 4 ft

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Step2: Check option 1

For side - lengths 2 ft, 2 ft, and 7 ft: $2 + 2=4<7$, so it cannot form a triangle.

Step3: Check option 2

For side - lengths 1 ft, 4 ft, and 6 ft: $1 + 4 = 5<6$, so it cannot form a triangle.

Step4: Check option 3

For side - lengths 3 ft, 2 ft, and 6 ft: $3+2 = 5<6$, so it cannot form a triangle.

Step5: Check option 4

For side - lengths 3 ft, 4 ft, and 4 ft:
$3 + 4=7>4$, $4 + 4 = 8>3$, $3+4 = 7>4$. It can form a triangle.

Answer:

The diagram with side - lengths 3 ft, 4 ft, and 4 ft.