The following side lengths, in meters, were given to a carpenter to build a front porch with a triangular design. The carpenter needs to determine which set of lengths will make a triangle to be able to use it in his design.
Option 1: Side lengths: 3, 3, 6
Option 2: Side lengths: 6, 8, 10
Option 3: Side lengths: 4, 6, 13 (1 point)
Option 1
Option 2
Option 3
Option 1 is not a valid triangle because the sum of the two shorter sides (3 + 3 = 6) is not greater than the longest side (6).
Option 2 is a valid triangle because the sum of the two shorter sides (6 + 8 = 14) is greater than the longest side (10).
Option 3 is not a valid triangle because the sum of the two shorter sides (4 + 6 = 10) is not greater than the longest side (13).
Therefore, only Option 2 (side lengths 6, 8, 10) will make a triangle that the carpenter can use in his design.
What is the length of the hypotenuse? If necessary, round to the nearest tenth.
C, Height = 6 ft., Base 8 ft.
C = ?
The length of the hypotenuse, C, can be found using the Pythagorean theorem:
C^2 = Height^2 + Base^2
Substituting the given values:
C^2 = 6^2 + 8^2
C^2 = 36 + 64
C^2 = 100
Taking the square root of both sides:
C = √100
C = 10
Therefore, the length of the hypotenuse, C, is 10 ft.
What is the length of the missing leg? If necessary, round to the nearest tenth.
B, Length = 6 ft., Height 8 ft.
B = ? Centimeters
To find the length of the missing leg B, we can again use the Pythagorean theorem:
B^2 = Length^2 + Height^2
Substituting the given values:
B^2 = 6^2 + 8^2
B^2 = 36 + 64
B^2 = 100
Taking the square root of both sides:
B = √100
B = 10
Therefore, the length of the missing leg B is 10 feet. If you need the length in centimeters, you can convert it. Since 1 foot is approximately 30.48 centimeters, the length of the missing leg B in centimeters would be 10 ft * 30.48 cm/ft ≈ 304.8 cm. Rounded to the nearest tenth, the approximate length in centimeters is 304.8 cm.
Aaliyah correctly used the diagram shown to explain the Pythagorean Theorem to a classmate. Which statement did Aaliyah use in her explanation?
A) 5 ^ 2 + 5 ^ 2 = 3 ^ 2
B) 3 ^ 2 + 4 ^ 2 = 5 ^ 2
C) 5 ^ 2 + 5 ^ 2 < 3 ^ 2
D) 3 ^ 2 + 4 ^ 2 > 5 ^ 2
[Choice A]
[Choice B]
[Choice C]
[Choice D]
The correct statement that Aaliyah used in her explanation is:
B) 3 ^ 2 + 4 ^ 2 = 5 ^ 2
This statement represents the Pythagorean theorem, where the sum of the squares of the two shorter sides (3 and 4) is equal to the square of the hypotenuse (5).