The sides AB, BC, and CA of a triangle ABC have 3, 4, and 5 interior points, respectively, on them. The number of triangles that can be constructed using these interior points as vertices is ___.

Open in App

Solution

We have total 3+4+5 = 12 points. So, number of $Δ s$ that can be formed using 12 such points is given by
Total number of ways of selecting three point - Number of ways three collinear points are selected
$=^{12} C_{3} -^{3} C_{3} -^{4} C_{3} -^{5} C_{3} = \frac{12 \times 11 \times 10}{6} - 1 - \frac{5 \times 4}{2 \times 1} = 220 - 15 = 205$

Suggest Corrections

Similar questions

Q. The sides

A B, B C

and

C A

of a triangle

A B C

have

3, 4

and

5

interior points, respectively on them. The number of triangles that can be constructed using these interior points as vertices is _______.

Q. The sides AB, BC, CA of a triangle ABC have

3, 4

and

5

interior points respectively on them. Find the number of triangles that can be constructed using these points as vertices.

Q. The sides AB, BC, CA of a triangle ABC have

3, 4

and

5

interior points respectively on them. The number of triangles that can be constructed using these points as vertices is-

The sides BC, CA and AB of a triangle ABC have 3, 4 and 5 interior points respectively on them. The number of triangles that can be constructed using these points as vertices is

Q. The sides

A B, B C, C A

of a trinagle

A B C

have

3, 4

and

5

interior point on them. The number of triangles that can be constructed using these points as vertices are

Join BYJU'S Learning Program

The sides AB, BC, and CA of a triangle ABC have 3, 4, and 5 interior points, respectively, on them. The number of triangles that can be constructed using these interior points as vertices is ___.

We have total 3+4+5 = 12 points. So, number of Δs that can be formed using 12 such points is given by Total number of ways of selecting three point - Number of ways three collinear points are selected =12C3−3C3−4C3−5C3=12×11×106−1−5×42×1=220−15=205