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DeltaPQR is an equilateral triangle. Seg...

`DeltaPQR` is an equilateral triangle. Seg `PS bot` side `QR` such that `Q-S-R`. Prove `PS^(2)=3QS^(2)` by completing the following activity.
In `DeltaPQS`,
`/_PSQ=square`……(Given)
`/_Q=square`………….(Angle of an equilateral triangle)
`:. /_QPS=30^(@)`.................(Remaining angle of `DeltaPQS`)
`:.DeltaPQS` is a `square` triangle
`PS=square PQ`.............(Side opposite to `60^(@)`)..............`(1)`
and `QS=square PQ`..........(Side opposite to `30^(@)`)
`PQ=2QS` .....`(2)`
Substituting value of `PQ` from `(2)` in `(1)`
`PS=(sqrt(3))/(2)xx2QS`
`:.PS=square QS`
`:.PS^(2)=3QS^(2)`......(Square both the sides)

A

`4QS^(2)`

B

`3QS^(2)`

C

`(3)/(2) QS^(2)`

D

`2QS^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
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