Math CentralQuandaries & Queries


Question from nekasia, a student:

what is the area of a rectangle with a diagonal of 8.5 inches PLEASE SHOW WORK


There are many different rectangles with different areas that all have a diagonal of length 8.5 inches. Let x be a positive number less than 8.5 and form a right triangle with one side of length x inches and a hypotenuse of length 8.5 inches. Let the length of the third side be y inches and complete the rectangle with side length x inches and y inches as in the diagram. The area of the rectangle is x × y square inches. Here is an example.

Let x = 3 then by Pythagoras theorem x2 + y2 = 8.52 and thus y2 = 8.52- 32 = 63.25 and y = √63.25 = 7.95 inches.Thus the area of the rectangle is x × y = 3 × 7.95 = 23.86 square inches.

Now you try a different value of x and see what area you get for the rectangle.


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