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Hello! No one on Brainly has been able to answer this question correctly so far, I've posted it thrice (it was answered once, but incorrectly - and the answer was expert verified!)

(Prime Factor Decomposition)
Shapes F and G are two different shapes that each have an area of 3^2 × 23^2 cm^2.
Shape G is a rectangle with integer side lengths. What is the smallest possible perimeter of shape G?
Give your answers in centimetres (cm).

To find the smallest possible perimeter of Shape G, we need to find out the dimensions of the rectangle that would result in an area of (3^2 times 23^2) square centimeters.

The prime factorization of (3^2 × 23^2) is (3^2 × 23^2 = 9 × 529).

For a rectangle, the perimeter is given by (2 ( length + width ))

Since we want to minimize the perimeter, we want to minimize both the length and the width.

The factors of 9 are 1, 3, and 9. The factors of 529 are 1, 23, and 529.

To minimize the perimeter, we can choose the dimensions of the rectangle to be 1 and 529. This gives us a perimeter of (2 (1 + 529) = 2 × 530 = 1060) centimeters.

So, the smallest possible perimeter of Shape G is 1060 centimeters.

merciemisiko merciemisiko · Answer 2 · 2024-03-31T12:02:45+02:00

Answer: 20 cm

Step-by-step explanation:

To find the smallest possible perimeter of shape G, we first need to determine the side lengths of the rectangle that would have an area of 3^2 × 23^2 cm^2.

The prime factorization of 3^2 × 23^2 cm^2 is 9×529

Therefore, the area of shape G is 9 cm^2 by 529 cm^2

To find the side lengths that would give this area with the smallest possible perimeter for a rectangle, look for factors of 529 and pair them up with factors of 9. This is because the perimeter of a rectangle is given by 2 × (length + width), and we want to minimize this expression.

The factors of 529 are: 1, 23 and 529.

The factors of 9 are: 1, 3, and 9.

Pairing up these factors, we find that the pairs with the smallest sum are (1,9) and (3,23)

Therefore, the possible side lengths for shape G are 1 cm by 9 cm or 3 cm by 23 cm. Since we are looking for the smallest possible perimeter, we choose the pair with the smaller sum, which is (1, 9).

The smallest possible perimeter of shape G is 2×(1+9)=20 cm.