The problem asks for the length of the diagonal of a rectangular frame with a length of 15 inches and a width of 8 inches. To solve this, we use the Pythagorean theorem:

$d = \sqrt{l^2 + w^2}$

Where:

• $d$ is the diagonal,
• $l = 15$ inches (length),
• $w = 8$ inches (width).

Substitute the values:

$d = \sqrt{15^2 + 8^2}$

$d = \sqrt{225 + 64}$

$d = \sqrt{289}$

$d = 17 \, \text{inches}.$

Thus, the length of the diagonal is 17 inches.

Would you like further clarification or a step-by-step explanation?

Here are 5 related questions:

1. What is the formula for the Pythagorean theorem, and how is it applied in real life?
2. How can you calculate the diagonal of a square if you only know one side?
3. What happens to the diagonal length if both length and width are doubled?
4. How would you determine the diagonal of a 3D rectangular prism?
5. What units are used when calculating the diagonal of a rectangle, and why?

Tip: Always double-check your calculations when applying the Pythagorean theorem to ensure accuracy!