The width of a rectangle is 6
inches, and the diagonal length of the rectangle is 15
inches.

Which measurement is closest to the length of the rectangle?
A.9
inches
B.
13.7
inches

C.21
inches
D.16.2
inches

To find the length of the rectangle, we can use the Pythagorean Theorem. The Pythagorean Theorem relates the width \(w\), length \(l\), and diagonal \(d\) of a rectangle as follows:

\[
d^2 = w^2 + l^2
\]

Where:
- \(w = 6 \, \text{inches}\)
- \(d = 15 \, \text{inches}\)
- \(l\) is the length of the rectangle (which we need to find).

Plugging in the values:

\[
15^2 = 6^2 + l^2
\]
\[
225 = 36 + l^2
\]
\[
225 - 36 = l^2
\]
\[
l^2 = 189
\]
\[
l = \sqrt{189} \approx 13.75 \, \text{inches}
\]

Thus, the length of the rectangle is approximately 13.7 inches.

The closest answer is **B. 13.7 inches**.

Would you like further details or have any questions?

Here are 5 related questions:
1. How does the Pythagorean theorem apply to different shapes?
2. What happens if the rectangle were a square?
3. Can the length ever be larger than the diagonal?
4. How would the formula change for a 3D object, such as a cuboid?
5. How would the solution change if the width was increased?

**Tip**: When dealing with right triangles, the diagonal (hypotenuse) is always the longest side.

The width of a rectangle is 6 inches, and the diagonal length of the rectangle is 15 inches. Which measurement is closest to the length of the rectangle? A. 9 inches B. 13.7 inches C. 21 inches D. 16.2 inches

Learn how to find the length of a rectangle with a width of 6 inches and a diagonal of 15 inches using the Pythagorean Theorem. This geometry problem demonstrates the application of key mathematical concepts and is suitable for students in Grades 7-10.

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