Prime Numbers Problem?

Question

2,3,5,7,11....are examples of prome numbers. Each number has only itself and 1 as factors. Suppose the number of units in eatch the length and widith of a rectangle are prime numbers and tehe perimiter is 36 units. What is the largest number of square units a number could have?

Answer 1

Hi,

If the perimeter is 36, then one length and one width have to add up to half of that or 18. Pairs of prime numbers that add to 18 are:

5 and 13 with an area of 65 square units
7 and 11 with an area of 77 square units <==

Dimensions are 7 x 11 for an area of 77 square units.

I hope that helps!! :-)

Answer 2

The largest area you could have is 81 sqft with a 9x9 square to get the 36 foot perimeter. However 9 is not prime, so go with the next available numbers that will add up to a 36 foot perimeter, 7 and 11. So the area is 77 sqft. Next is 13 and 5, but that only gives 65 sqft, so the 7x11 rectangle is your answer.

Answer 3

Since the perimeter is 36 units then 2l + 2w = 36 --> l + w = 18.

The possible combinations for this are:

(5, 13) & (7, 11)

So:

5 * 13 = 65
7 * 11 = 77

The largest possible number of square units is 77 square units.

Answer 4

Length plus width sums to 36/2 = 18. You're looking to maximize their product.

There aren't a lot of choices, since one of the numbers has to be odd and less than or equal to 18/2 = 9. The only pairs that work are (7,11) and (5,13). Since 77 > 65, 77 is your answer.

Answer 5

77