SOLUTION: A boulder stops a surveyor from directly measuring the boundary AB of a piece of land. He measures AC=500 feet and extends it 10 feet to a point D. BC turns out to be 600 feet and

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Question 1112637: A boulder stops a surveyor from directly measuring the boundary AB of a piece of land. He measures AC=500 feet and extends it 10 feet to a point D. BC turns out to be 600 feet and extending it 12 feet to reach point E. What is the length of AB if ED is 8 feet?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The sketch below (not to scale) illustrates the situation.
The sketch is purposely not to scale, because triangle DEC is so small compared to triangle ABC, that making DEC to scale would make it almost invisible.
Triangles ABC and DEC must have been designed by the surveyor
so as to be similar triangles.
Their angles at C are congruent because they are vertical angles.
sides EC and DC were made to be proportional to BC and AC respectively:
BC%2FEC=600ft%2F%2212+ft%22=50 and
AC%2FDC=500ft%2F%2210+ft%22=50 .
Because there is obe pair of congruent angles at C,
flanked by pairs of proportional sides,
triangles ABC and DEC are similar triangles "by SAS similarity".
DEC is a scale down version of ABC,
with all lengths in ABC being 50 times greater.
So, AB%2FED=50
AB%2F%228+ft%22=50
AB=50%288ft%29
highlight%28AB=400ft%29 .