Optimization

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joey123

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Oct 23, 2005
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A rectangle is inscribed ina an isosceles right traingle whose hypotenuse is 2 units long. What is the largest area the rectangle can have and what are its dimensions? Use optimization to answer this question.
 
Where are you stuck? You've drawn the right triangle and labelled the hypotenuse with the given length of 2, and used your knowledge of triangles to find the lengths of the two legs. You've drawn the rectangle inside the triangle, and used variables to label the length and the width. You've noticed that the rectangle, in touching the legs at its corners, cuts off similar triangles, and... then what?

Please reply with specific details of what you have tried and where you are stuck. Thank you.

Eliz.
 
So what did you do with the similar triangles?

Please reply showing your steps. Thank you.

Eliz.
 
So you didn't find any right triangles when you drew the rectangle on the hypotenuse of the right triangle, with its corners touching the legs? Then you need to try redrawing, because you need this picture in order to get started.

Eliz.
 
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