Are all rectangles whose diagonals are 19 in. long congruent?

Question

about congruent rectangles

Answer 1

No.  There are an infinite number of counter examples to this conjecture.

 

19^2 = 361

 

x^2 + y^2 = 361

 

For any combination of x and y (the length and width of a rectangle) as long as the sum of each squared are equal to 361 will give you a rectangle with a diagonal of 19in.  Any 2 different combinations would give you 2 non-congruent rectangles.

Answer 2

If you have multiple rectangles that have diagonals drawn inside them, and the diagonals are the same length, then the rectangles will be the same size.  Therefore, the rectangles are congruent.

 

The size of a diagonal is directly  proportionate to the rectangle size.