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SAT - Math - Geometry

A summer camp counselor wants to find a length, x, in feet, across a lake as represented in the sketch above.

 

A summer camp counselor wants to find a length, x, in feet, across a lake as represented in the sketch above. The lengths represented by AB, EB, BD and CD on the sketch were determined to be 1800 feet, 1400 feet, 700 feet, and 800 feet, respectively. Segments AC and DE intersect at B, and the angle AEB and the angle CBD have the same measure. What is the value of x?

∠ABE = ∠CBD (Vertically Opposity angles)

∠BEA = ∠BDC (Given)

thus triangle ABE ~ triangle CBD

thus

BE/BD = AE/CD

1400/700 = x / 800

x = 1600 ft.