Question

Briana’s backsplash in her kitchen is made up of square tiles like the one below. The tiles are white with a black diagonal stripe. Which of the following would help her find x, the length of the black stripe?

square with length 4 inches and a diagonal line

Answer 1

To find \( x \), the length of the black diagonal stripe in a square tile with a side length of 4 inches, you can analyze the geometry of the situation.

1. **Understanding the diagonal of the square**: In a square, the diagonal can be found using the Pythagorean theorem. For a square with side length \( s \), the diagonal \( d \) can be calculated using the formula:
\[
d = s \sqrt{2}
\]
In this case, since the side length \( s \) is 4 inches:
\[
d = 4 \sqrt{2}
\]

2. **Finding \( x \)**: The black diagonal stripe runs from one corner of the tile to the opposite corner. Therefore, the length \( x \) of the black stripe is the same as the length of the diagonal. Hence,
\[
x = 4 \sqrt{2}
\]
To find a numerical approximation, you can calculate:
\[
x \approx 4 \times 1.414 \approx 5.656 \text{ inches}
\]

So, the length of the black diagonal stripe is \( 4 \sqrt{2} \) inches, which is approximately 5.656 inches.