Final answer:
To solve for the length of the rectangle, we define the width as w inches and the length as w + 3 inches. Using the perimeter formula 2l + 2w = 34 inches, we solve for w, which is found to be 7 inches. Thus, the length of the rectangle is 10 inches.
Step-by-step explanation:
To find the length of the rectangle when the length is 3 inches more than its width and the perimeter is 34 inches, first, let's define the width of the rectangle as w inches. Therefore, the length will be w + 3 inches. The perimeter P of a rectangle is given by P = 2l + 2w, where l is the length and w is the width. Given the perimeter is 34 inches, we can set up the equation:
- 2(w + 3) + 2w = 34
- 2w + 6 + 2w = 34
- 4w + 6 = 34
- 4w = 34 - 6
- 4w = 28
- w = 28 / 4
- w = 7 inches
Now, using the width to find the length, we calculate:
- Length = w + 3 = 7 + 3
- Length = 10 inches
Therefore, the length of the rectangle is 10 inches.