Final answer:
By using the Pythagorean theorem, we calculate that the length of the shortest side of the rectangular frame is approximately 13.2 inches.
Step-by-step explanation:
To find the length of the shortest side of the rectangular frame, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
The diagonal of the rectangle acts as the hypotenuse, and the two sides of the rectangle are the other two sides of the right-angled triangle. Given the length of the diagonal (hypotenuse) as 20 inches and one side as 15 inches, we can denote the length of the shortest side as x.
According to the Pythagorean theorem:
- 15² + x² = 20²
- 225 + x² = 400
- x² = 400 - 225
- x² = 175
- x = √175
- x ≈ 13.2 inches (rounded to the nearest tenth)
Therefore, the length of the shortest side is approximately 13.2 inches.