Knowledge You Can Build On — Est. 1998
Friday[+1!] Puzzler -- Rectangle
Alex Y
Pictured below are a rectangle and two right triangles inscribed in it. What are the dimensions of the rectangle?
There are no tricks here--everything is as it appears on the drawing. And the math involved is some we all learned in junior high or middle school. Still, I found it pretty hard to solve.
Re: Friday[+1!] Puzzler -- Rectangle
Larry Barrett
The long side is 25. That is easy. The lower triangle is 15 20 25.
To get the short side of the rectangle requires finding lots of angles and tangents and inverse tangents. If I did it correctly the short side is 16.67.
Correct! (but no trig is required)
Alex Y
You got it, but all that is required is Pythagoras and similar triangles. The tricky part is that you are not measuring either end line, but another line that is the same length.
No-trig solution
Alex Y
Draw a vertical line through F, and label its endpoints G (bottom) and H. Pythagorus gives you the missing dimensions on the partially measured right triangles. The portion of each triangle to the right of GH is a similar right triangle.
BFC is a 3-4-5 right triangle, with sides 15, 20, and 25.
FGC is similar, with a hypotenuse of 20, so the missing sides are 12 (GF) and 16 (GC)
AED has sides 7, 24, and 25
FHD is similar, with side HD = 16
FH = 7*16/24 = 14/3 = 4 2/3
So GH =12+4 2/3 
