If `AOBC` is a rectangle whose three vertices are `A(0,3)`,`O(0,0)` and `B(5,0)`, then find the length of its diagonal.

Options

A. `5`
B. `3`
C. `sqrt(34)`
D. `4`

Answer

C

Explanation

Now , length of the diagonal AB= Distance between the points A(0,3) and B(5,0).
`:.` Distance between the points `(x_(1),y_(1))and (x_(2),y_(2)),`
d`=sqrt((x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2))`
Here , `x_(1)=0,y_(1)=3andx_(2)=5,y_(2)=0`
`:.` Distance between the points A(0,3) and B(5,0)
AB `=sqrt((5-0)^(2)+(0-3)^(2))`
`=sqrt(25+9)=sqrt(34)`
Hence, the required length of its diagonal is `sqrt(34)`.