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

Subscribe to:
Post Comments (Atom)

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)

----------------------------------

(d/2)² = x² + h² ( from tr OHD )

d² = 4x² + 4h²

D² + d² = D² + 4x² + 4h² (2)

------------------------------

comparing (1) & (2) give the results