Question

1. the width of a rectangle is 6 less than the length, and if the perimeter

a) 23 b) 13 c) 17 d) 7

Explanation:

The problem seems incomplete as the perimeter value is not fully provided. But assuming a common problem (e.g., perimeter is 40, a typical value for such problems), we can proceed. Let length be \( l \), width \( w = l - 6 \). Perimeter of rectangle is \( P = 2(l + w) \). Substitute \( w \): \( P = 2(l + l - 6)=2(2l - 6)=4l - 12 \). If we assume \( P = 40 \) (since problem is cut off, but for demonstration), then \( 4l - 12 = 40 \), \( 4l = 52 \), \( l = 13 \), then \( w = 13 - 6 = 7 \)? Wait, no, maybe the perimeter was supposed to be given. Since the original problem's perimeter part is cut, but looking at options, maybe the perimeter is 40 (common). Wait, maybe the full problem is "the perimeter is 40, find length or width". Let's check options. If length is 13, width is 7, perimeter is 2*(13+7)=40. So maybe the question is to find length or width. But since the problem is incomplete, but assuming standard problem:

Step1: Define variables

Let length \( = l \), width \( = l - 6 \)

Step2: Perimeter formula

Perimeter \( P = 2(l + w) = 2(l + l - 6) = 4l - 12 \)

Step3: Assume perimeter (since not given, but options suggest). Let's say \( P = 40 \) (common). Then \( 4l - 12 = 40 \)

Step4: Solve for \( l \)

\( 4l = 52 \) → \( l = 13 \) (matches option B). Then width \( = 13 - 6 = 7 \) (option D). But maybe the question was to find length, so answer B) 13.

Answer:

Assuming the perimeter is 40 (common in such problems), the length is 13, so B) 13.