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The perimeter of a triangle with vertices (0, 4) (0, 0) and (3, 0) is:
- a)15
- b)12
- c)8
- d)10
Correct answer is option 'B'. Can you explain this answer?
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The perimeter of a triangle with vertices (0, 4) (0, 0) and (3, 0) is:...
To find the perimeter of a triangle, we need to calculate the sum of the lengths of all its sides.
Given vertices:
A (0, 4)
B (0, 0)
C (3, 0)
Step 1: Calculate the distance between points A and B
The distance formula between two points (x1, y1) and (x2, y2) is given by:
d = √[(x2 - x1)² + (y2 - y1)²]
Using the distance formula, we can calculate the distance between points A and B:
dAB = √[(0 - 0)² + (0 - 4)²]
= √[0 + 16]
= √16
= 4
Step 2: Calculate the distance between points B and C
Using the distance formula, we can calculate the distance between points B and C:
dBC = √[(3 - 0)² + (0 - 0)²]
= √[9 + 0]
= √9
= 3
Step 3: Calculate the distance between points C and A
Using the distance formula, we can calculate the distance between points C and A:
dCA = √[(3 - 0)² + (0 - 4)²]
= √[9 + 16]
= √25
= 5
Step 4: Calculate the perimeter
The perimeter of a triangle is the sum of the lengths of its sides.
Perimeter = dAB + dBC + dCA
= 4 + 3 + 5
= 12
Therefore, the perimeter of the triangle with vertices (0, 4), (0, 0), and (3, 0) is 12 units. Hence, the correct option is B) 12.
Given vertices:
A (0, 4)
B (0, 0)
C (3, 0)
Step 1: Calculate the distance between points A and B
The distance formula between two points (x1, y1) and (x2, y2) is given by:
d = √[(x2 - x1)² + (y2 - y1)²]
Using the distance formula, we can calculate the distance between points A and B:
dAB = √[(0 - 0)² + (0 - 4)²]
= √[0 + 16]
= √16
= 4
Step 2: Calculate the distance between points B and C
Using the distance formula, we can calculate the distance between points B and C:
dBC = √[(3 - 0)² + (0 - 0)²]
= √[9 + 0]
= √9
= 3
Step 3: Calculate the distance between points C and A
Using the distance formula, we can calculate the distance between points C and A:
dCA = √[(3 - 0)² + (0 - 4)²]
= √[9 + 16]
= √25
= 5
Step 4: Calculate the perimeter
The perimeter of a triangle is the sum of the lengths of its sides.
Perimeter = dAB + dBC + dCA
= 4 + 3 + 5
= 12
Therefore, the perimeter of the triangle with vertices (0, 4), (0, 0), and (3, 0) is 12 units. Hence, the correct option is B) 12.
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The perimeter of a triangle with vertices (0, 4) (0, 0) and (3, 0) is:a)15b)12c)8d)10Correct answer is option 'B'. Can you explain this answer?
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