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PQRS is a parallelogram in which PR is p...

PQRS is a parallelogram in which PR is perpendicular to QS. If PR=8cm and QS=6 cm, then find PS

A

5cm

B

4cm

C

7cm

D

6cm

Text Solution

Verified by Experts

The correct Answer is:
A
PQRS is a parallelogram and `PR bot QS`.
`:. ` PQRS is a rhombus.

Given , PR=8 cm and
QS= 6 cm . In a rhombus, the diagram bisect to each other.
Let O be the point of intersect of PR and QS
`:. PO=(PR)/(2)=4 cm `
`OS=(QS)/(2)= 3cm `
`(PS)^(2)=(OP)^(2)+(OS)^(2)` ( `:.` POS form right triangle )
`=4^(2)+3^(2)=16+9=25=5^(2)`
`implies PS=5cm`
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