geometry

(See attached files for full problem description)

What is the length of the hypotenuse...

What is the length of the hypotenuse of the rigth triangle ABC in examination figure,if AC=6 and AD=5 note : draw a triangle A B C and the heigth from point C to D,the point D is in between A and B,the distance between A and D is 5 and the distance between A and C is 6

Showing sum of lines drawn are equal to height

Hi, I need help with a straight forward geometry problem. Given an equilateral triangle, pick any point on the interior and draw lines that are perpendicular out to each side, and show that the sum of these perpendicular lines equal the height of the triangle.

Make a venn diagram

Make a venn diagram: 25 students play soccer, 4 boys play soccer and baseball, 3 girls play soccer and baseball, 10 boys play baseball, 4 girls play baseball, 3 boys plays baseball and tennis, 1 girl plays baseball and tennis, 1 boy plays all three sports, 1 girl plays all three sports, 9 students play tennis, 3 boys play soccer and tennis, 3 girls play soccer and tennis, 12 girls play at least one of the 3 sports.

How many of the 500 students are enrolled in all three classes?

500 students enrolled in at least 2 of 3 classes: English, Math, History. 150 students enrolled in both history and English, 300 enrolled in math & history, 170 enrolled in both math and English. How many of the 500 students are enrolled in all three classes?