Solution (Not Yet!) to Gifted World Challenge #5 - Mar 30- Apr 26, 2024

Hello everyone!

Many of you correctly identified that 2 rectangles (4x4 and 6x3) have the same numerical value of area and perimeter, but nobody has provided a proof that these are the only 2 rectangles that satisfy the condition.

So we are extending the challenge by 2 more weeks- put on your thinking caps and give this a shot- try and prove this! Please submit your responses through the google form (link below)

The Question

Perimeter and area obviously have different units , but is it possible to have two rectangles in which their numerical values are equal ? If so, how many such rectangles are there and what are their dimensions? Assume the side lengths of the rectangles are natural numbers i.e. 1,2,3.... not fractional or decimal values.

You are NOT allowed to use algebra in answering this question.

You can submit your answer here. Even if you don't manage to answer this question completely, share whatever you have done and what you plan to investigate next. How you think is more important than getting the right answer quickly!

The last day to submit your answer is Friday, April 26, 2024.

(Note that commenting is disabled on this post so that nobody gives away the answer to someone who hasn't solved it yet)