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??
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.
To determine the length and width of Jennifer's rectangle, we need to find two numbers whose product is 48 and when added together, result in a prime number.
1. Start by finding the factors of 48.
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
2. Now, let's find the sum of each pair of factors and check if it results in a prime number.
Sum of factors:
1 + 48 = 49 (not prime)
2 + 24 = 26 (not prime)
3 + 16 = 19 (prime)
From the above calculations, we can see that the sum of 3 and 16 results in the prime number 19.
3. Since Jennifer added the length and width of her rectangle to get a prime number, we can conclude that 3 and 16 are the length and width respectively.
Therefore, the length of Jennifer's rectangle is 16 units and the width is 3 units.
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.