Question

The coordinates of the vertices of a triangle are \( (0,6) \), \( (0,0) \) and \( (8,0) \). Then the perimeter of the triangle is:

• A. \(14\)
• B. \(24\)
• C. \(42\)
• D. none of these

Hint:

When vertices lie on axes, two sides are axis-aligned (lengths are easy), and the third can often form a Pythagorean triple.

Answer 1

The Correct Option is B

Step 1: Find the side lengths using the distance formula.
\[ AB: (0,6)\text{ to }(0,0) \Rightarrow \sqrt{(0-0)^2+(6-0)^2}=6.\] \[BC: (0,0)\text{ to }(8,0) \Rightarrow \sqrt{(8-0)^2+(0-0)^2}=8.\] \[CA: (8,0)\text{ to }(0,6) \Rightarrow \sqrt{(8-0)^2+(0-6)^2}=\sqrt{64+36}=10. \]
Step 2: Add the side lengths to get the perimeter.
\[ \text{Perimeter} = 6+8+10 = 24. \]
Step 3: Conclude.
Hence, the perimeter of the triangle is \(24\).