Question

What is the length of the longest side of a triangle that has the vertices (-3, 2), (3, 2), and (3, 6)?

A. 5 units
B. 2√ ̅13 units
C. 2√ ̅15 units
D. √ ̅5 units

Answer 1

@bibby

Answer 2

If you can see the diagram, it shows the approximation of the three points.
The lines between them form a right triangle, since two of the points are on y=2 and two points are on x=3. So, in a right triangle the longest side has to be the hypotenuse, which is between (3, 6) and(-3,2).
To calculate the distance between the two, you can either use the distance formula, or since this is a right triangle, the Pythagorean theorem. The Pythagorean theorem is easier, it goes like this: a^2 + b^2 = c^2
a and b are the two shorter legs and c is the hypotenuse.
so (from the diagram) : 4^2+6^2= c^2
16+36=c^2
52=c^2
\[\sqrt{52}\]=
\[\sqrt{13*4}\]=
\[2\sqrt{13}\] That's it! Hope that helps!