steven is cutting an 11 ft piece of lumber into three pieces to build a triangular garden. which diagram…

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?\n2 ft 2 ft 7 ft\n1 ft 4 ft 6 ft\n3 ft 2 ft 6 ft\n3 ft 4 ft 4 ft

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?\n2 ft 2 ft 7 ft\n1 ft 4 ft 6 ft\n3 ft 2 ft 6 ft\n3 ft 4 ft 4 ft

Answer

Explanation:

The problem requires us to identify which set of three lumber pieces, cut from an 11 ft piece, can form a triangle. For three lengths to form a triangle, they must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side. Also, the sum of the lengths of the three pieces must equal the total length of the lumber, 11 ft.

Step1: Check Option 1 (2 ft, 2 ft, 7 ft)

First, verify if the sum of the lengths is 11 ft. $2 + 2 + 7 = 11 \text{ ft}$ Next, apply the triangle inequality theorem. Let $a=2$, $b=2$, $c=7$. Is $a + b > c$? $2 + 2 > 7$ $4 > 7$ (False) Since one condition of the triangle inequality theorem is not met, these lengths cannot form a triangle.

Step2: Check Option 2 (1 ft, 4 ft, 6 ft)

First, verify if the sum of the lengths is 11 ft. $1 + 4 + 6 = 11 \text{ ft}$ Next, apply the triangle inequality theorem. Let $a=1$, $b=4$, $c=6$. Is $a + b > c$? $1 + 4 > 6$ $5 > 6$ (False) Since one condition of the triangle inequality theorem is not met, these lengths cannot form a triangle.

Step3: Check Option 3 (3 ft, 2 ft, 6 ft)

First, verify if the sum of the lengths is 11 ft. $3 + 2 + 6 = 11 \text{ ft}$ Next, apply the triangle inequality theorem. Let $a=3$, $b=2$, $c=6$. Is $a + b > c$? $3 + 2 > 6$ $5 > 6$ (False) Since one condition of the triangle inequality theorem is not met, these lengths cannot form a triangle.

Step4: Check Option 4 (3 ft, 4 ft, 4 ft)

First, verify if the sum of the lengths is 11 ft. $3 + 4 + 4 = 11 \text{ ft}$ Next, apply the triangle inequality theorem. Let $a=3$, $b=4$, $c=4$.

  1. Is $a + b > c$? $3 + 4 > 4$ $7 > 4$ (True)
  2. Is $a + c > b$? $3 + 4 > 4$ $7 > 4$ (True)
  3. Is $b + c > a$? $4 + 4 > 3$ $8 > 3$ (True) All conditions of the triangle inequality theorem are met, so these lengths can form a triangle.

Answer:

D. 3 ft, 4 ft, 4 ft