math
posted by syd on .
jennifer has made a rectangle using 48 square titles. if she adds the length and width of her rectangle together she gets a prime number . what is the length and width of jennifers rectangle??

You might try squaring a few numbers; i.e., 2^2= 4
3^2 = 9
4^2 = 16
5^2 = 25
etc.
Now look at the prime numbers; i.e., 2, 3, 5,7,11,13,17,19,23, etc.
Which of the "squares" will divide evenly into 48? Add those sides together to see if the sum is a prime number. 
so the area must be 48 square units, where the length and width are whole numbers
so factors of 48 would be
1x48
2x24
3x16
4x12
6x8
the sums of these possibilites are
49,26,19,16, and 14
of these only 19 is a prime number
so the length of Jennifer's triangle is 16 and its width is 3 
Phillip is thinking of a number that is less than 20 and has 3 factor pairs. Phillip also says that if he adds together the factors in the factor pairs he gets 19, 11, and 9. What is Phillips number? Explain how you found your answer.