Question
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?
Answers
black_widow
AB=50
stranger
how
black_widow
Let length of AB =a
sABC=sABD+sACD (s stands for area)
1/2x60x(a^2-30^2)^0.5=1/2x(16a+32a)
5(a^2-30^2)^0.5=4a
25a^2-16a^2=25x30^2
a^2=2500
a=50
sABC=sABD+sACD (s stands for area)
1/2x60x(a^2-30^2)^0.5=1/2x(16a+32a)
5(a^2-30^2)^0.5=4a
25a^2-16a^2=25x30^2
a^2=2500
a=50