Question

What is the length of the longest side of a triangle that has vertices at (-4,2), (-4,6), and (4,2)?

Answer 1

As seen from the picture,
`\triangle \mathrm{ABC}` is rectangular, then, by the Pythagoras' theorem:

`\mathrm{BC}^2=\mathrm{AB}^2+\mathrm{AC}^2\medskip\\\mathrm{BC}^2=4^2+8^2=16+64=80\medskip\\\mathrm{BC}=√(80)=√(16\cdot 5)=4√(5)`

Answer 2

4√5

Explanation:

The triangle with the vertices given is a right triangle, as shown on the grid below.

Therefore, the length of the hypotenuse is the length of the longest side of the triangle.

The base of the triangle measures 8 units, and the height of the triangle measures 4 units. Use the Pythagorean theorem to find the length of the hypotenuse.

Therefore, the length of the longest side of the triangle measures units.