Question

The area of a square is given as (s3)6.

What is its perimeter?

Answer 1

The area of a square is given by the side length squared, so to find the perimeter of a square with area (s^3)^6, we find the side length by taking the square root of the area which results in s^9, then multiply by 4 to get the perimeter: 4s^9.

Step-by-step explanation:

The area of a square is provided as (s3)6. To find the perimeter of the square, we must first determine the side length of the square by finding the square root of the area. The area of a square is equal to the side length squared (A = s2), so we can equate (s3)6 to s2 and solve for s. Once we have the side length, we can find the perimeter by multiplying the side length by 4 (P = 4s).

First, we simplify the area expression: (s3)6 = s18. Next, we take the square root to find the side length: s9. The perimeter of the square will then be 4 × s9.

It is important to note that the units will also be raised to the ninth power, so if s was measured in meters, the perimeter would have units of meters to the ninth power, which seems like a non-standard scenario. This suggests there may have been a typo or misunderstanding in the original question, but we will disregard that for this explanation.

Answer 2

Step-by-step explanation:

what does this problem description really say ? what is the area of that square ?

36 ?

s3×6 ?

s³×6 ?

5³×6 ?

2³×6 ?

(5×3)×6 ?

(2×3)×6 ?

and these are just the options that I can see right away without really thinking about it.

in any case, the solution is to draw the square root of the area, and then multiply the result by 4.

why ?

because the area of a square is the square of the length of one of its side - like for any rectangle the area is length×width, but in a square length = width, so the area is length×length = length².

therefore, sqrt(area) = sqrt(length²) = length.

and the perimeter of the square is the way all around the whole square (4 sides), which is then

length + length + length + length = 4×length

from all the possibilities I listed up there, only 36 and (2×3)×6 lead to nice round numbers.

as the area would be in both cases 36.

sqrt(36) = 6

and the perimeter would be 6×4 = 24