Nekasia,

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.

Penny