Proposed Problem
See complete Problem 251 at:
gogeometry.com/problem/p251_parallelogram_diagonal_square_area.htm
Level: High School, SAT Prep, College geometry
Post your solutions or ideas in the comments.
Monday, February 16, 2009
Problem 251. Parallelogram, sides, diagonals, squares, areas
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name B → S2'side, b → S1'side
ReplyDeletename D → S3'side, d → S4'side
name h → altitude DH, H on AC
name x → OH
B² = ( D/2 + x)² + h² ( from tr ADC, P theorem )
B² = D²/4 + Dx + x² + h²
b² = ( D/2 - x )² + h²
b² = D² - Dx + x² + h²
2 ( B² + b² ) = D² + 4x² + 4h² (1)
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(d/2)² = x² + h² ( from tr OHD )
d² = 4x² + 4h²
D² + d² = D² + 4x² + 4h² (2)
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comparing (1) & (2) give the results