Final answer:
To find the area of a rectangle with a perimeter of 58 inches and its length being 5 inches more than its width, we set up and solve equations based on the relationship between perimeter, length, and width. We find the width to be 12 inches and the length to be 17 inches. The area of the rectangle is calculated as 204 square inches.
Step-by-step explanation:
To find the area of the rectangle given the perimeter and the relationship between its length and width, we first need to use the information provided to establish equations. The perimeter (P) of a rectangle is given by P = 2l + 2w, where l is the length and w is the width.
We are told that the perimeter is 58 inches and that the length is 5 inches more than its width. This can be represented by the equations:
- P = 2l + 2w = 58 inches
- l = w + 5 inches
Substituting the second equation into the first gives us:
- 58 = 2(w + 5) + 2w
- 58 = 2w + 10 + 2w
- 58 = 4w + 10
- 48 = 4w
- w = 12 inches
Now that we have the width, we can find the length:
l = w + 5 = 12 inches + 5 inches = 17 inches
Finally, the area of a rectangle is defined as Area = length × width, thus:
Area = 17 inches × 12 inches = 204 square inches.