Answer: C) 14
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Work Shown:
Draw a vertical line through point C. This vertical line crosses line segment ED to form point F. I've shown this point in blue. Refer to the diagram below.
Focus on the triangle CFD. This is a right triangle with the 90 degree angle at point F.
Triangle CFD has the vertical red portion equal to 12 units, since segment EB is 12 units (note how quadrilateral BCFE is a rectangle).
Segment FD is ED-BC = 17-10 = 7 units long.
Let's apply the pythagorean theorem to find the hypotenuse CD
a^2 + b^2 = c^2
(CF)^2 + (FD)^2 = (CD)^2
(12)^2 + (7)^2 = (CD)^2
144 + 49 = (CD)^2
193 = (CD)^2
(CD)^2 = 193
CD = sqrt(193)
CD = 13.8924439894499 approximately
CD = 14
When rounding to the nearest whole number, segment CD is approximately 14 units long.
