Let PQR be a triangle which PQ = 3. Form the vertex R, draw the altitude RS to meet PQ at S. Assume that `RS=sqrt3" and " Ps=QR`. Then PR equals

Options

A. `sqrt5`
B. `sqrt6`
C. `sqrt7`
D. `sqrt8`

Answer

C

Explanation

`PS=QR`
`PS + SQ = 3`
in `DeltRSQ" "Sq=3-PS=3-QR`
`QR^(2)=RS^(2)+SQ^(2)`
`QR^(2)=3+(3-QR)^(2)`
`QR^(2)=3+9+QR^(2)-6QR`
`6QR=12`
`QR=2`
`SQ=1" "PS=2`
in `DeltaRSP`
`PR^(2)=RS^(2)+PS^(2)`
`=3+4`
`PR^(2)=7`
`PR=sqrt7`