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In triangle A B C , if angle is 90^0 and...

In triangle `A B C` , if angle is `90^0` and the area of triangle is `30 sqdot` units, then the minimum possible value of the hypotenuse `c` is equal to (a) `30sqrt(2)` (b) `60sqrt(2)` (c) `120sqrt(2)` (d) `2sqrt(30)`

A

`30sqrt(2)`

B

`60sqrt(2)`

C

`120sqrt(2)`

D

`2sqrt(30)`

Text Solution

Verified by Experts

The correct Answer is:
D
`Delta=(1)/(2)ab`
`rArr ab=60`
`b=c cos theta, a=c sin theta`
`rARr Delta=(1)/(2)c^(2)sintheta cos theta=(c^(2)sin2theta)/(4)`
`=30`
or `c^(2)=120co sec 2 theta`
or `c_("min")^(2)=120`
or `c_("min")=2sqrt(30)`.
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