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An isosceles right triangle has area 8 c...

An isosceles right triangle has area 8 `cm^(2)`. The length of its hypotenuse is

A

`sqrt32` cm

B

`sqrt16` cm

C

`sqrt48` cm

D

`sqrt24`

Text Solution

Verified by Experts

The correct Answer is:
A
(a) Given, area of an isosceles right triangle= 8 `cm^(2)`
Area of an isosceles triangle `=(1)/(2)" "(Base xx Height)`
`rArr8=(1)/(2)" "(BasexxBase)`
`[because"Base=height, as triangle is an isosceles triangle"]`n
`rArr (Base)^(2)=16rArrBase = 4cm`
`In triangleABC, "using Pythagoras theorem,"`
`AC^(2)=AB^(2)+BC^(2)=4^(2)+4^(2)=16+16`
`rArrAC^(2)=32rArrAC=sqrt32 cm`
`["taking positive square root becuase legth is always positive"]`
Hence the length of its hypotenuse is `sqrt32 cm.`
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