Question

Let ABCD be a parallelogram whose equations for the diagonals AC and BD are x+2y = 3 and 2x+y = 3, respectively. If length of diagonal AC = 4 units and area of parallelogram ABCD = 8 sq. units then The length of BC is equal to

(a) \(\frac{2\sqrt{10}}{3}\)

(B) \(\frac{4\sqrt{10}}{3}\)

(C) \(\frac{8\sqrt{10}}3\)

(d) None

Answer 1

In Δ CPB, cosθ \(=\frac{PC^2+PB^2-BC^2}{2.PC.PB}\)

BC = \(\frac{2\sqrt{10}}3\)