The two adjacent sides of a parallelogram are represented by the lines x-y+1=0 and 4 x-3 y=2. If one of the diagonal of the parallelogram is the line y=(3 x/2), then find the area of parallelogram.

Question

The two adjacent sides of a parallelogram are represented by the lines x-y+1=0 and 4 x-3 y=2. If one of the diagonal of the parallelogram is the line y=(3 x/2), then find the area of parallelogram. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Here, tan θ=|((4/3)-1/1+(4)3)|=(1/7), where θ is the angle between adjacent sides of given parallelogram. So, area of parallelogram = p 1 p 2 operatornamecosec θ=((3/√2))((3/2))(5 √2)=9 (square units) where p1, p2 are distances between opposite parallel sides of parallelogram.

Q. The two adjacent sides of a parallelogram are represented by the lines x−y+1=0 and 4x−3y=2. If one of the diagonal of the parallelogram is the line y=23x​, then find the area of parallelogram.

Here, tanθ=∣∣​1+34​34​−1​∣∣​=71​, where θ is the angle between adjacent sides of given parallelogram. So, area of parallelogram =p1​p2​cosecθ=(2​3​)(23​)(52​)=9 (square units) where p1​,p2​ are distances between opposite parallel sides of parallelogram.

Q. The two adjacent sides of a parallelogram are represented by the lines $x - y + 1 = 0$ and $4 x - 3 y = 2$ . If one of the diagonal of the parallelogram is the line $y = \frac{3 x}{2}$ , then find the area of parallelogram.