How many triangles 4 5 6

Reset your password if you forgot it. Geometry: Triangles Geometry. Solvers Solvers. This gives 18, or 3 times 6 triangles. Remember high school math? Johanna Mangahas, Ph. I could have made this much easier on readers—and, crucially, much easier on my inbox—had I just sketched the triangle on plain, white computer paper. But no. I unfortunately drew this triangle on lined paper, and lots of smart people have correctly pointed out that, well, actually , if you count the light blue parallel lines in the image in addition to the dark blue lines written in marker, there are actually more than 18 total triangles here—considerably more.

I never specified to only use those dark blue lines, and thus, I am wrong. You are right. One reader, Ralph Linsangan, totally owned me by sending this image, in which he marks every additional triangle found under the technicality, flagging 17 additional triangles for a total of That kind of dedication is just one of many reasons I love Popular Mechanics readers. Until the next teaser! Outstanding point , Poingly.

Add a comment. Active Oldest Votes. Algebra beyond this point corrected. Brian M. Scott Brian M. Scott k 51 51 gold badges silver badges bronze badges. Using these rules, you can extend the table above arbitrarily. Which sounds just like what you're asking. References If you want to know how to obtain that formula without looking it up, or how to check that formula without simply trusting an encyclopedia, then some of the references given at OEIS will likely help you out: J.

Conway and R. Guy, The Book of Numbers, p. Gerrish, How many triangles , Math. Halsall, An interesting series , Math. Larsen, The eternal triangle — a history of a counting problem , College Math. Hamberg and T. Green, An application of triangular numbers , Mathematics Teacher, 60 , Referenced by Larsen B.

Mastrantone, Comment , Math. Problem , Math. Martin Sleziak MvG MvG As such, the entries on the diagonal correspond to closed loops of size 3. By virtue of the Pythagorean Theorem, in a right triangle the sum of the squares of the smaller two sides equals the square of the largest side. Only 9, 12, and 15 fit this rule. What is a Triangle? Because the angles are always in that ratio, the sides are also always in the same ratio to each other. The best known triple is , with being the next most recognized.

Any triangle composed of sides of lengths that match the Pythagorean triple will be a right triangle. That means our triangle has a 90 degree angle for angle C. Therefore, 6, 8, 10 and 15, 20, 25, among countless others, would represent sides of a right triangle. Hypotenuse, opposite, and adjacent.