Question

If the vertices of a triangle have rectangular coordinates \((0,0)\), \((8,0)\), and
\((8,6)\), respectively, then the perimeter of the triangle is

• A. \( \text{10} \)
• B. \( \text{14} \)
• C. \( \text{24} \)
• D. \( \text{36} \)
• E. \( \text{48} \)

Hint:

Sum the distances between all vertex pairs.

Answer 1

The Correct Option is C

Step 1: Calculate side lengths using distance formula
\( \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).
Step 2: Side 1: \((0,0)\) to \((8,0)\), \( \sqrt{(8-0)^2 + (0-0)^2} = 8 \).
Side 2: \((8,0)\) to \((8,6)\), \( \sqrt{(8-8)^2 + (6-0)^2} = 6 \).
Side 3: \((0,0)\) to \((8,6)\), \( \sqrt{(8-0)^2 + (6-0)^2} = \sqrt{64 + 36} = 10 \).
Step 3: Perimeter = \( 8 + 6 + 10 = 24 \).
Step 4: (C) 24 matches the sum.