An isosceles triangle with base 10 and sides 13. What is the total length of the red line segments?
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The total length is 120/13, which is approximately 9,23.
First, the height of the triangle is easily found by the Pythagorean theorem: h=√(132-52)=12. Therefore its area is 10*12/2=60.
Next, acknowledge that triangle ABC is the union of triangles ADC and BDC, the heights of which are a and b respectively and which both have base 13. Their total area is (a+b)*13/2. Equating this with 60 gives the desired result.
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