A learner claims that a square with 7cm and a rectangle measuring 5cm by 9cm have the same perimeter calculate both perimeter and determine whether the claim is correct

The perimeter of a square is given by the formula $P_{\text{square}} = 4 \times \text{side}$.

Given side length = 7 cm.
$P_{\text{square}} = 4 \times 7\ \text{cm}$
$P_{\text{square}} = 28\ \text{cm}$

The perimeter of the square is $\boxed{28\ \text{cm}}$.

The perimeter of a rectangle is given by the formula $P_{\text{rectangle}} = 2 \times (\text{length} + \text{width})$.

Given length = 9 cm and width = 5 cm.
$P_{\text{rectangle}} = 2 \times (9\ \text{cm} + 5\ \text{cm})$
$P_{\text{rectangle}} = 2 \times (14\ \text{cm})$
$P_{\text{rectangle}} = 28\ \text{cm}$

The perimeter of the rectangle is $\boxed{28\ \text{cm}}$.

Perimeter of the square = 28 cm
Perimeter of the rectangle = 28 cm

Since the perimeter of the square (28 cm) is equal to the perimeter of the rectangle (28 cm), the learner's claim is correct.

The learner's claim is $\boxed{\text{correct}}$.