question_answer

If A (-3, 0) and C (5, 2) are the end points of diagonal AC of rectangle ABCD, with B on the x- axis, the perimeter of the rectangle ABCD is

A)  20                           

B)         24

C)  28                         

D)         30

Correct Answer: A

Solution :

 Here, it is given that \[A(-3,0)\] and \[C(5,2)\] are the endpoints of the diagonal AC of rectangle ABCD. Let us draw a figure as per given information.                 x - co-ordinate of B and C are same. y - co-ordinate of C and D are same. Co-ordinates of \[D=(-3,2)\] Since B is on x - axis, so y - co-ordinate of B will be 0, and x - co-ordinate of B and C are same. Co-ordinates of \[B:(5,0)\] Now, in rectangle ABCD                 \[AD=(2)-(0)=2\] \[\Rightarrow \]               \[BC=AD=2\]. and        \[CD=(5)-(-3)=8\] \[\Rightarrow \]               \[AB=CD=8.\] Hence, perimeter of the rectangle \[ABCD=2(AB+BC)=2(8+2)=20\]