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 the sum of its three side lengths.

Answer 1

The Correct Option is C

Using the distance formula to find the sides:
\[ AB = \sqrt{(0-0)^2 + (4-0)^2} = \sqrt{16} = 4. \] \[ BC = \sqrt{(3-0)^2 + (0-0)^2} = \sqrt{9} = 3. \] \[ CA = \sqrt{(3-0)^2 + (0-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5. \] \[ \text{Perimeter} = AB + BC + CA = 4 + 3 + 5 = \]