A rectangle has an area of 48 centimeters squared and a perimeter of 38 centimeters. What are the dimensions of the rectangle?

Answer 1

Let's assume the length of the rectangle is L centimeters and the width is W centimeters.
The formula for the area of a rectangle is A = L × W.
Accordingly, we have LW = 48. ----(1)
The formula for the perimeter of a rectangle is P = 2(L + W).
Therefore, 2(L + W) = 38.
Hence, L + W = 19. ----(2)
We can solve this system of equations to find the dimensions of the rectangle.
From (2), we can determine that W = 19 - L and substitute it into equation (1).
Then, LW = 48 becomes L(19 - L) = 48.
Expanding the equation, we obtain:
19L - L^2 = 48.
Rearranging it, we get L^2 - 19L + 48 = 0.
Factoring the quadratic equation, we have (L - 16)(L - 3) = 0.
Therefore, L = 16 or L = 3.
When L = 16, W = 19 - 16 = 3.
And when L = 3, W = 19 - 3 = 16.
So, the dimensions of the rectangle are 16 cm × 3 cm or 3 cm × 16 cm.