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The sides of a triangle are 35 cm, 54 cm...

The sides of a triangle are `35` `cm`, `54` `cm` and `61` `cm`, respectively. The length of its longest altitude

A

`16sqrt5` cm

B

`10sqrt5` cm

C

`24sqrt5` cm

D

28 cm

Text Solution

Verified by Experts

The correct Answer is:
C
(c) Let ABC be a triangle in which sides AB=35 cm, BC=54 cm and CA=61 cm

Now, semi-perimeter of a triangle,
`s=(a+b+c)/(2)=(35+54+61)/(2)=(150)/(2)=75 cm`
`[because"semi-perimeter",s=(a+b+c)/(2)]`
`because"Area of" triangleABC=sqrt(s(s-a)(s-b)(s-c))`
`=sqrt(75(75-35)(75-54)(75-61))`
`=sqrt(75xx40xx21xx14)`
`=sqrt(25xx3xx4xx2xx5xx7xx3xx7xx2)`
`=5xx2xx2xx3xx7sqrt5=240sqrt5cm^(2)`
`"Also", " Area of"triangleABC=(1)/(2)xxABxx"Altitude"`
`rArr (1)/(2)xx35xxCD=420sqrt5`
`rArr CD=(420xx2sqrt5)/(35)`
`therefore CD=24sqrt5`
Hence, the length of altitude is `24sqrt5 cm.`
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