The length of the hypotenuse of a right isosceles triangle is 4√3 What is the perimeter of the triangle?

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Answer 1 · 2015-06-14T00:16:58

Permeter#=16.7#

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Answer 2 · 2015-06-15T13:35:10

The perimeter of the triangle is " "#color(blue)16.72616 # units.

Perimeter=AB+BC+CA

#P=AB+AC+4sqrt(3)# [since AC=hypotenuse]

#P=AC+AC+4sqrt(3)#[since it is a isosceles triangle]

#p=2AC+4sqrt(3)# #" "color(blue) ((1))#

#sintheta#=opposite side/hypotenuse

#sin45^@=(AC)/(CB)#

#AC=(BC)xxsin45^@#

#AC=(BC)xx1/(sqrt(2))#[from angle table]

#AC=(4sqrt(3)xx1/sqrt2)#

#AC=(4sqrt3)/(sqrt2)#

substitute the above value in #" "color(blue) ((1))#

#P=(2xx(4sqrt3)/sqrt2)+(4sqrt3)#

#P=((8sqrt3)/sqrt2)+4sqrt3#

#P=# #color(blue)16.72616 # units.