Question

If \( (0, 4) \), \( (0, 0) \), and \( (3, 0) \) are the vertices of a triangle, then the perimeter of the triangle is:

• A. 8
• B. 10
• C. 12
• D. 15

Hint:

The perimeter of a triangle is simply the sum of the lengths of its sides, which can be calculated using the distance formula.

Answer 1

The Correct Option is C

The given vertices of the triangle are \( A(0, 4) \), \( B(0, 0) \), and \( C(3, 0) \).
To find the perimeter of the triangle, we calculate the lengths of the three sides using the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
First, we calculate the length of \( AB \): \[ AB = \sqrt{(0 - 0)^2 + (4 - 0)^2} = \sqrt{16} = 4 \]
Then, we calculate the length of \( BC \): \[ BC = \sqrt{(3 - 0)^2 + (0 - 0)^2} = \sqrt{9} = 3 \]
Finally, we calculate the length of \( AC \): \[ AC = \sqrt{(3 - 0)^2 + (0 - 4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \]
Now, we can calculate the perimeter of the triangle: \[ \text{Perimeter} = AB + BC + AC = 4 + 3 + 5 = 12 \]