answer to travis has designed a rectangle with an area of 59 square units. his rectangle is the smallest rectangle with whole number side lengths. what are the length and width of the rectangle, explain your reasoning. what is the perimeter of the rectangle? explain your reasoning

1 by 59

59 is not divisible by any other whole numbers.

P = 2L + 2W
P = ?

To find the length and width of Travis's rectangle, we need to consider the factors of the given area (59 square units).

The factors of 59 are 1 and 59. Since Travis's rectangle is the smallest rectangle with whole number side lengths, the length and width must be as close to each other as possible.

So, we can try the possible side lengths using the factors. Let's start with 1 unit wide and 59 units long. However, the product of these dimensions (1 x 59) is 59, which is not equal to the given area of 59 square units.

Next, let's try 2 units wide and 29.5 units long. We can see that 29.5 is not a whole number, so it doesn't meet the requirement for whole number side lengths.

Now, let's try 3 units wide and 19.67 units long. Again, 19.67 is not a whole number.

We continue this process until we find a whole number length.

When we try 4 units wide, we get a length of 14.75 units. This is also not a whole number length.

Finally, when we try 5 units wide, we get a length of 11.8 units. This is still not a whole number length.

However, when we try 6 units wide, we get a length of 9.83 units. Again, not a whole number length.

By trying different widths, we can see that the closest we get to whole number lengths is with 7 units wide.

When we use 7 units as the width, the length would be 8.43 units (approximately). Since no exact whole number length is possible, this is the best option.

Therefore, the length of the rectangle is approximately 8.43 units and the width is 7 units.

To find the perimeter of the rectangle, we add up all the sides in units.

Perimeter = 2 * (length + width)

Substituting the values we found:

Perimeter = 2 * (8.43 + 7)
Perimeter = 2 * 15.43
Perimeter = 30.86 units

So, the perimeter of Travis's rectangle is approximately 30.86 units.

Please note that the lengths and perimeter are approximations since we are limited to whole number side lengths.

To find the length and width of the rectangle, we need to find two whole numbers whose product is equal to the given area of 59 square units.

One way to do this is to find all the pairs of factors of 59 and then determine which pair gives us the smallest rectangle. Since 59 is a prime number, it only has two factors: 1 and 59. Therefore, the only possible pair of factors is (1, 59).

Thus, the dimensions of the rectangle are 1 unit by 59 units. We can see that this is the smallest rectangle with whole number side lengths that has an area of 59 square units.

To find the perimeter of the rectangle, we add the lengths of all four sides. The formula for the perimeter of a rectangle is P = 2(length + width). In this case, the length is 59 units and the width is 1 unit. Hence, the perimeter P = 2(59 + 1) = 2(60) = 120 units.