It's urgent for you to come to the meeting In the triangle ABC, D is a point on the side of BC, if AB = 10, BD = 6, ad = 8, AC = 17 Judge whether the triangle ABC is a right triangle Finding the area of triangle ABC In the triangle ABC, the angle ACB = 90 degrees, BC = 3, AC = 4, CD is perpendicular to AB, and the perpendicular foot is d If the lengths a, B and C of triangle ABC satisfy a + B + C + 200 = 12a + 16b + 20c, try to judge the shape of triangle ABC

It's urgent for you to come to the meeting In the triangle ABC, D is a point on the side of BC, if AB = 10, BD = 6, ad = 8, AC = 17 Judge whether the triangle ABC is a right triangle Finding the area of triangle ABC In the triangle ABC, the angle ACB = 90 degrees, BC = 3, AC = 4, CD is perpendicular to AB, and the perpendicular foot is d If the lengths a, B and C of triangle ABC satisfy a + B + C + 200 = 12a + 16b + 20c, try to judge the shape of triangle ABC

Topic 1: from ab = 10, BD = 6, ad = 8, the triangle abd is a right triangle (according to Pythagorean theorem)
Ad vertical BC
So ACD is a right triangle
So according to Pythagorean theorem, DC = 15
Because AC = 17, ab = 10, BC = BD + DC = 6 + 15 = 21, Pythagorean theorem does not hold
So triangle ABC is not a right triangle
Area of ABC = BC * ad / 2 = 21 * 8 / 2 = 84
Topic 2
Because the angle ACB = 90 degrees, BC = 3, AC = 4
So according to Pythagorean theorem, ab = 5
According to the triangle area formula, AB * CD / 2 = BC * AC / 2
CD = 12 / 5
In right triangle BCD, according to Pythagorean theorem, BD = 9 / 5
Topic 3
A + B + C + 200 = 12a + 16b + 20c
(a-12a + 36) + (b-16b + 64) + (c-20c + 100) = 0
(a-12a + 6) + (b-16b + 8) + (c-20c + 10) = 0
(a-6) + (B-8) + (C-10) = 0
So (a-6) square = 0; (B-8) square = 0; (C-10) square = 0
So a = 6; b = 8; C = 10
So triangle ABC is a right triangle (6 + 8 = 10)