The total perimeter of a square frame is 52 cm. The length of a rectangular board is equal to the side of the square frame, and its width is 5 cm less than its length. Find the area of the rectangular board.

The correct answer is 104 cm².

Step 1: Find the side length of the square frame.
The perimeter of a square is given by the formula:
$\text{Perimeter}=4\times \text{side}$
Given that the total perimeter of the square frame is 52 cm:
$4\times \text{side}=52\text{cm}$
$\text{side}=\frac{52}{4}=13\text{cm}$

Step 2: Determine the dimensions of the rectangular board.
The length of the rectangular board is equal to the side of the square frame:
$\text{Length}\left(l\right)=13\text{cm}$
The width of the rectangular board is 5 cm less than its length:
$\text{Width}\left(w\right)=13-5=8\text{cm}$

Step 3: Calculate the area of the rectangular board.
The area of a rectangle is calculated using the formula:
$\text{Area}=\text{Length}\times \text{Width}$
Substituting the values of length and width:
$\text{Area}=13\text{cm}\times 8\text{cm}=104\text{cm}{2}^{}$

Thus, the area of the rectangular board is 104 cm².