Categories Intermediate Lopsided Post author By Rik Post date September 20, 2022 1 Comment on Lopsided Lopsided The apex of a parabola is the shared vertex of two rectangles. Proof that the rectangles are similar. Scroll down for a solution to this problem. Solution Solution by Ignacio Larrosa Cañestro. Please leave this field empty Don’t miss these puzzles! Subscribe to the weekly geometry puzzle e-mail. Email Address * Check your inbox or spam folder to confirm your subscription. Tags parabola, rectangle ← Harmonic proportions → The fried egg One reply on “Lopsided” A little more direct solution: Slope of dotted line = (a^2-c^2)/(a+c) = a -c. b = slope*c + d = (a-c)c + c^2 = ac. Thus b/a = ac/a = c, and d/c = c^2/c = c, and rectangles have the same shape. Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Email * Website Save my name, email, and website in this browser for the next time I comment. Δ Optionally add an image (JPEG only)

A little more direct solution: Slope of dotted line = (a^2-c^2)/(a+c) = a -c. b = slope*c + d = (a-c)c + c^2 = ac. Thus b/a = ac/a = c, and d/c = c^2/c = c, and rectangles have the same shape.

## One reply on “Lopsided”

A little more direct solution:

Slope of dotted line = (a^2-c^2)/(a+c) = a -c.

b = slope*c + d = (a-c)c + c^2 = ac.

Thus b/a = ac/a = c, and d/c = c^2/c = c, and rectangles have the same shape.