The perimeter of a rectangle is 54 cm. The area of the same rectangle is 176 cm². What are the dimensions of the rectangle?
(1 point)
Let the length of the rectangle be L cm and the width be W cm.
Since the perimeter of a rectangle is calculated by adding all four sides, we can set up the equation 2L + 2W = 54.
The area of a rectangle is calculated by multiplying the length and width, so we can set up the equation L * W = 176.
From the first equation, we can isolate L by dividing both sides by 2: L + W = 27.
We can then isolate W by subtracting L from both sides: W = 27 - L.
Substituting this value of W into the second equation, we get L * (27 - L) = 176.
Expanding the equation, we have 27L - L^2 = 176.
Rearranging the equation, we get L^2 - 27L + 176 = 0.
We can factor this quadratic equation as (L - 16)(L - 11) = 0.
Setting each factor equal to zero, we find L = 16 or L = 11.
If L = 16, then the width W = 27 - 16 = 11.
If L = 11, then the width W = 27 - 11 = 16.
Therefore, the possible dimensions of the rectangle are 16 cm by 11 cm or 11 cm by 16 cm.