Question

8 multiple choice 5 points
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?
option 1: 2 ft, 2 ft, 7 ft
option 2: 1 ft, 4 ft, 6 ft
option 3: 3 ft, 2 ft, 6 ft
option 4: 3 ft, 4 ft, 4 ft

Explanation:

Step1: Recall triangle inequality rule

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

Step2: Test Option 1 (2 ft, 2 ft, 7 ft)

Check sums:
$2 + 2 = 4$, and $4 < 7$ → Violates the rule.

Step3: Test Option 2 (1 ft, 4 ft, 6 ft)

Check sums:
$1 + 4 = 5$, and $5 < 6$ → Violates the rule.

Step4: Test Option 3 (3 ft, 2 ft, 6 ft)

Check sums:
$3 + 2 = 5$, and $5 < 6$ → Violates the rule.

Step5: Test Option 4 (3 ft, 4 ft, 4 ft)

Check sums:
$3 + 4 = 7 > 4$,
$4 + 4 = 8 > 3$,
$3 + 4 = 7 > 4$ → Satisfies the rule.

Answer:

D. 3 ft, 4 ft, 4 ft