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

Options

A. `30sqrt(2)`
B. `60sqrt(2)`
C. `120sqrt(2)`
D. `2sqrt(30)`

Answer

D

Explanation

`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)`.