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PQRS is are rectangle of dimensions 12 c...

PQRS is are rectangle of dimensions 12 cm and 5 cm. PMNR is a rectangle drawn is such a way that the diagonal PR of the first rectangle is one of its sides and side opposie to it is touching the first rectangle at S as shown in figure. What is the ratio of the area of rectangle PQRS to that of PMNR?

A

`3:1`

B

`2:3`

C

`1:1`

D

`5:4`

Text Solution

Verified by Experts

The correct Answer is:
C
Draw a line ST perpendicular to PR.
Since PQRS is a rectangle in `DeltaPQR`, we have

`PR^(2)=PQ^(2)+QR^(2)` (By Pythagoras theorem)
`impliesPR^(2)=(12)^(2)+(5)^(2)=169`
`impliesPR=13cm`
Now area of `DeltaPSR=1/2xx` base`xx` height
`implies1/2xxSTxxPR=1/2xxPSxxSR`
`implies1/2xxSTxx13=1/2xx5xx12impliesST=60/13cm`
Also `PM=ST=60/13cm`
Area of rectangle `PQRS =PQxxQR`
`=(12xx5)cm^(2)=60cm^(2)`
Area of rectangle PMNR=MN`xxPM`
`=(13xx60/13)cm^(2)=60cm^(2)`
`:.` Required ratio `=60/60` i.e. 1:1
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