Determine 82724
A right triangle has an area of 36 cm2. A square is placed in it so that two sides of the square are parts of two sides of a triangle, and one vertex of the square is in a third of the longest side.
Determine the area of this square.
Determine the area of this square.
Correct answer:
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Math student
Given: (ab)/2 = 36; ab = 72
Let: c = sqrt(aˆ2 + bˆ2)
(b-x)/(c/3) = x/((2c)/3)); b = (3x)/2
(a-x)/((2c)/3)) = a/c; a = 3x
ab = (3x)((3x)/2) = 72
Therefore, xˆ2 = 16.
Let: c = sqrt(aˆ2 + bˆ2)
(b-x)/(c/3) = x/((2c)/3)); b = (3x)/2
(a-x)/((2c)/3)) = a/c; a = 3x
ab = (3x)((3x)/2) = 72
Therefore, xˆ2 = 16.
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