Final answer:
To determine the dimensions of a rectangle with an area of 48 cm² and a perimeter of 38 cm, we use systems of equations to find that the dimensions are 16 cm by 3 cm.
Step-by-step explanation:
To find the dimensions of a rectangle given its area is 48 cm² and its perimeter is 38 cm, we can set up a system of equations. Let the length be 'l' and the width be 'w'. The area A of a rectangle is given by the formula A = l × w, and the perimeter P is given by P = 2l + 2w.
From the information given we have:
Divide the perimeter equation by 2 to simplify:
We can solve for one variable in terms of the other. Let's solve for w:
Substitute this into the area equation:
Now we solve the quadratic equation:
Thus, the length 'l' can be either 3 cm or 16 cm. If l = 3 cm, then w = 19 - 3 = 16 cm, and if l = 16 cm, then w = 19 - 16 = 3 cm.
Therefore, the dimensions of the rectangle are 16 cm by 3 cm.