Est. 1998 — 27 years of woodworking knowledge
Friday Puzzler -- Triangle area
Alex Y
In the following drawing, all the shapes that look like squares are. Accidentally left off the drawing--the sides of the large square are length 5. What is the area of the blue triangle? No trig or "heavy" geometry or algebra required.
Re: Friday Puzzler -- Triangle area
Kent B
Is the plane BU or BD????
LOL! BU
Since a square is a two dimensional box,
Larry Barrett
I guess we can say that Kent is thinking outside of the square.
Re: Friday Puzzler -- Triangle area
Larry Barrett
I think one way to calculate the area involves a lot of square roots. My answer is (with rounding errors) is 2.38.
Sorry, but no
Alex Y
No square roots required, and answer off by more than rounding.
Re: Sorry, but no
Larry Barrett
Well, still using same approach (which involves lots of square roots but is pretty straightforward) but with more accuracy, my revised answer is 1.93.
Re: Sorry, but no
Alex Y
Closer, but correct methods (there are actually a couple of variants) yield an exact answer, with no square roots needed.
Re: Sorry, but no
Larry Barrett
Third try. I believe the area is 2. No square roots involved.
Correct!
And I am sure you saw
Alex Y
that the size of the large square is irrelevant. I just threw in the 5x5 size to divert from resizing that square, which makes solutions easier to see.
Re: And I am sure you saw
Larry Barrett
You are giving me too much credit (in addition to several hints). I did not see that large square could have sides = x and still have same area for the triangle until just now. This is an interesting problem.
I am surprised that my square root approach did not yield a result closer to the correct answer. The approach is correct, I think, although I needed to know that the larger square is 5x5. I used the fact that if you know three sides of a triangle you can calculate the area using Heron's formula. I found the length of each side using Pythagoras, which resulted in all the square roots.