SOLUTION: a non-square rectangle is inscribed in a square so that each vertex of the rectangle is at the trisection point of the different sides of the square. find the ratio of the area of

Algebra ->  Rectangles -> SOLUTION: a non-square rectangle is inscribed in a square so that each vertex of the rectangle is at the trisection point of the different sides of the square. find the ratio of the area of       Log On


   

Question 1178368: a non-square rectangle is inscribed in a square so that each vertex of the rectangle is at the trisection point of the different sides of the square. find the ratio of the area of the rectangle to the area of the square.
Answer by ikleyn(52946) About Me  (Show Source):
You can put this solution on YOUR website!
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a non-square rectangle is inscribed in a square so that each vertex of the rectangle is at the trisection point
of the different sides of the square. find the ratio of the area of the rectangle to the area of the square.
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Let the side of the square be "a" units.


We then have 4 (four) right-angled triangles outside the rectangle,

each having one leg of  a%2F3  units long and the other leg of  2a%2F3  units long.


The area of each such a triangle is  %281%2F2%29%2A%28a%2F3%29%2A%28%282a%29%2F3%29%29 = a%5E2%2F9.


The area of 4 (four) such triangles is  %284a%5E2%29%2F9.


Thus the area of the rectangle to the area of the square is  5%2F9.    ANSWER

Solved.