SOLUTION: A square is inscribed into a right-angled triangle with length sides 3, 4 and 5 so that it lies along both legs and just touches the hypotenuse. Find the length of the square.

Question 1164601: A square is inscribed into a right-angled triangle with length sides 3, 4 and 5 so that it lies along both legs and just touches the hypotenuse. Find the length of the square.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A square is inscribed into a right-angled triangle with length sides 3, 4 and 5 so that it lies along both legs and just touches the hypotenuse. Find the length of the square.
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x = side of the square
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Area of the 3-4-5 triangle is 6 sq units.
Area of the square is x^2 sq units.
Area of the smaller triangle on the side of 3 units is x*(3-x)/2
Area of the triangle on the side of 4 units is x*(4-x)/2
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x*(3-x)/2 + x*(4-x)/2 + x^2 = 6
Solve for x

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