Question

name
lesson 1 cool-down area and multiples
if a rectangle is 6 tiles wide, what could be
6×7 = 42 (with red x) 6×6 =
explain or show your reasoning.
if a rectangle has a

Explanation:

Step1: Recall the area formula of a rectangle

The area of a rectangle is given by \( A = \text{length} \times \text{width} \). Here, the width is 6 tiles. Let the length be \( l \) (in tiles), so the area \( A = 6 \times l \).

Step2: Determine possible lengths and areas

The length \( l \) can be any positive integer (assuming we use whole - tile lengths). For example, if \( l = 1 \), then \( A=6\times1 = 6 \) square tiles. If \( l = 2 \), then \( A = 6\times2=12 \) square tiles. If \( l = 3 \), then \( A=6\times3 = 18 \) square tiles. If \( l = 4 \), then \( A = 6\times4 = 24 \) square tiles. If \( l = 5 \), then \( A=6\times5=30 \) square tiles. If \( l = 7 \), then \( A = 6\times7 = 42 \) square tiles (the first calculation is correct in terms of the formula, maybe the red cross was a mistake in the original work, or maybe there was a mis - understanding of the problem's constraints). If \( l = 6 \), then \( A=6\times6 = 36 \) square tiles.

In general, any multiple of 6 (since \( A = 6l \)) can be the area of the rectangle when the width is 6 tiles, and the length \( l \) can be any positive real number (if we don't restrict to whole tiles), but for the case of tile - based (probably whole - number) lengths, the length is a positive integer and the area is a multiple of 6.

Answer:

If the rectangle has a width of 6 tiles, and let the length be \( l \) tiles, the area \( A = 6l \). For example, if \( l = 7 \), \( A=6\times7 = 42 \) square tiles; if \( l = 6 \), \( A = 6\times6=36 \) square tiles. Any positive integer value for the length (in tiles) will give a valid area as a multiple of 6. (If we consider the first calculation \( 6\times7 = 42 \), it is a correct application of the rectangle area formula \( A=\text{width}\times\text{length} \) with width = 6 and length = 7.)