The garden is to be paved with the triangular tiles all over. How many such…
2023
The garden is to be paved with the triangular tiles all over. How many such tiles can be formed from a vertices point of the ground at a distance of 14 points and 7 of which lies in the straight lines.
- A.
533
- B.
333
- C.
329
- D.
None of these
Attempted by 20 students.
Show answer & explanation
Correct answer: C
We have 14 points in the plane, of which 7 lie on a single straight line. A triangle is formed by any 3 non-collinear points.
Step 1: Count all ways to choose 3 points from 14: C(14,3) = (14 × 13 × 12) / 6 = 364
Step 2: Count triples that are collinear (from the 7 collinear points): C(7,3) = (7 × 6 × 5) / 6 = 35
Step 3: Subtract collinear triples from total triples to get the number of triangles: 364 − 35 = 329
Answer: 329 triangles