Final answer:
The student is tasked with finding the length and width of a doormat given its area and perimeter. By setting up equations for the area and perimeter, and using substitution, the student can solve for the two unknowns, which are the dimensions of the doormat.
Step-by-step explanation:
You're trying to find the dimensions of a doormat with a known area and perimeter. The area of the doormat is 420 square inches, and the perimeter is 86 inches.
This is a standard algebra problem that involves setting up equations based on the properties of rectangles—that is, the area (A) of a rectangle is the product of its length (l) and width (w), and the perimeter (P) is twice the sum of the length and width.
Let's assign variables to the unknown dimensions: l (length) and w (width). The two equations based on the given area and perimeter are:
- A = l * w, which gives us 420 = l * w
- P = 2l + 2w, which gives us 86 = 2l + 2w
Divide the perimeter equation by 2 to simplify it:
Now you can express w in terms of l: w = 43 - l. Substitute this into the area equation:
Expanding this and solving the resulting quadratic equation will give you the values of l and w, which are the dimensions of the doormat you're looking for.
The complete question is: The area of a doormat is 420 square inches. The perimeter is 86 inches. What are the dimensions of the doormat? is: