How do you find the length of the legs of a 45°-45°-90° triangle with a hypotenuse of 4* sqrt 2 cm.?

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Answer 1 · 2015-12-10T10:26:55

The two legs are long #4#.

If #AB# and #BC# are the legs, then you know that

#AB^2+BC^2=AC^2#

Since we have a #45^@# - #45^@# - #90^@# triangle, the triangle is isosceles, and so the two legs are equal. This means that the formula becomes

#2AB^2=AC^2#

And we know that #AC=4sqrt(2)#, so #AC^2=16*2=32#. Thus,

#2AB^2=32#

#AB^2=16#

#AB=4#