Unecessary and additional lines.
Geometry
Level
4
The respective lengths of the red line and the green line are 65 and 56. What is the length of the blue line?
The answer is 33.
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1 solution
If x & y are the segments of the diagonal then by application of Stewart's Theorem to the lower triangle, we get: x(65)²+y(65)²=(x+y)(56²+xy) or xy=65² - 56²=(121)(9). From the upper triangle, (Blue Line)² = xy = (121)(9) or Blue Line = (11)(3) = 33