first: A diagonal of a rectangle is the square root of 13 meters and the area of the rectangle is 6 meters squared. What are the dimensions of the rectangle?
last: Find the ordered triple of nonzero digits (A,B,C) for which (AA)squared=BBCC where AA and BBCC are respectively, two-digit and four-digit base-ten numerals.
The way to solve these problems is with some intelligent guessing and checking. For the first, if the rectangle is x meters by y meters then, by the theorem of Pythagoras you know that x2 + y2 = 13. Can you find two interger x and y so that x2 + y2 = 13? Is xy = 6?
For problem 2, 30 x 30 = 900 so the fact that AA2 has four digits implies that A is larger than 3. Calculate 442, 552,... looking for a four digit answer of the form BBCC.Cheers,