Final answer:
To find the length of the picture frame, the Pythagorean theorem is used. After calculating, the length is approximately 12.04 inches, which suggests option B) 13 inches is most accurate.
Step-by-step explanation:
The question asks to determine the length of a picture frame given the diagonal and the height. To solve this, 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. In this case, the diagonal is the hypotenuse, and the height and the length are the other two sides.
We have:
- Diagonal (hypotenuse) = 17 inches
- Height = 12 inches
- Length (to be found)
The Pythagorean theorem can be written as:
c2 = a2 + b2
Substituting the known values, we have:
172 = 122 + length2
To find the length, we solve for the length2:
172 - 122 = length2
289 - 144 = length2
145 = length2
Now take the square root on both sides to find length:
√145 = length
About 12.04 = length
So, the length of the picture frame is approximately 12.04 inches, which is closest to the option B) 13 inches.