Justine
secondary student

2 questions

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.

Thanks

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.