Question

The line 6x+8y=48 intersects the corridinate axes A and B respectvely.A line L bisects the area and perimeter of triangle OAB where O is origin.The number of possible lines is ?​

Answer 1

The number of possible lines is one.

Step-by-step explanation:

From question, the equation of the line given is:

6x + 8y = 48 → (equation 1)

Now, the line intercepts x axis and y axis at A(8, 0) and B(0, 6).

The area of triangle OAB is given as:

∴ A = 1/2 × 8 × 6 = 24 units²

The hypotenuse of the triangle is given as:

⇒ AB = √(8² + 6²) = 10 units

Now, the perimeter of triangle is:

P = OA + OB + OC = 8 + 6 + 10

∴ Perimeter = 23 units

The line from the origin is given by the equation,

y = mx where, m = 1

y = x ⇒ x - y = 0 → (equation 2)

On solving equation (1) and (2), we get,

∴ x = 48/14

The point D is given as (24/7, 24/7)

Area of ΔOAD  = Area of ΔOBD

Perimeter of ΔOAD = Perimeter of ΔOBD

Thus, one line is possible.