GEOMetry(TRIANGLE)
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ABC is an isosceles triangle where AB=AC and BC=60. D is a point on BC such that the perpendicular distance from D to AB and AC is 16 and 32, respectively. What is the length of AB?

AB=50

how

Let length of AB =a
sABC=sABD+sACD (s stands for area)
1/2x60x(a^230^2)^0.5=1/2x(16a+32a)
5(a^230^2)^0.5=4a
25a^216a^2=25x30^2
a^2=2500
a=50