Question

In a rhombus ABCD if BC=8x-10 and CD=3x+10 find the sides of rhombus

Answer 1

Answer:

Correct option is D)

Let the coordinate of A be (0,α).

Since the sides AB and AD are parallel to the lines y=x+2 and y=7x+3 respectively.

Therefore the diagonal AC is parallel to the bisector of the angle between these two lines.

The equation of the bisectors are given by,

2

x−y+2

=±

50

7x−y+3

⇒5(x−y+2)=±(7x−y+3)

⇒2x+4y−7=0 and 12x−6y+13=0

Thus, the diagonals of the rhombus are parallel to the lines

2x+4y−7=0 and 12x−6y+14=0

Therefore slope of AE=−

4

2

or

6

12

⇒

1−0

2−α

=−

2

1

or

1−0

2−α

=2

⇒α=

2

5

or α=0