the shortest altitude of triangle with side 52cm, 56cm, 60cm is-:
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Here sides of Δ are 52cm, 56cm, 60cm
So, semi perimeter, s = 52+56+60/2
s = 84 cm
Acc. to Heron's formula
Ar(Δ) =√s(s-a)(s-b)(s-c)
. = √84(84-52)(84-56)(84-60)
. = √84*32*28*24
. =√1806336 cm²
. =1344 cm²
Also ar(Δ) = 1/2*base*height
So, if we will take 60cm as the base then only we will get shortest possible height(altitude)
So, 1/2*60*h = 1344
. 30h = 1344
. h = 1344/30
. h= 44.8 cm
So the correct answer is (a) 44.8cm
So, semi perimeter, s = 52+56+60/2
s = 84 cm
Acc. to Heron's formula
Ar(Δ) =√s(s-a)(s-b)(s-c)
. = √84(84-52)(84-56)(84-60)
. = √84*32*28*24
. =√1806336 cm²
. =1344 cm²
Also ar(Δ) = 1/2*base*height
So, if we will take 60cm as the base then only we will get shortest possible height(altitude)
So, 1/2*60*h = 1344
. 30h = 1344
. h = 1344/30
. h= 44.8 cm
So the correct answer is (a) 44.8cm
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