Ted is making three picture frames like the one shown below. What length of wood does Ted need for all three picture frames?
a) 11 1/2in, b) 15 3/4in, c) 27 1/4,
d) 81 3/4 in.
The length is 7 7/8 in., and width is 5 3/4in.
P = 2L + 2W
Multiply the perimeter of one frame by 3 to find the total amount of wood needed.
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To find the total length of wood Ted needs for all three picture frames, we first need to determine the perimeter of one picture frame.
The perimeter of a rectangle is given by the formula P = 2(length + width). In this case, the length of the picture frame is 7 7/8 inches, and the width is 5 3/4 inches.
Adding these lengths together, we get:
P = 2(7 7/8 + 5 3/4)
P = 2(63/8 + 23/4)
P = 2(63/8 + 46/8)
P = 2(109/8)
P = 109/4
So the perimeter of one picture frame is 109/4 inches.
To find the total length of wood Ted needs for all three picture frames, we multiply the perimeter of one picture frame by 3 (since he is making three frames):
Total length of wood = 3 * (109/4)
Total length of wood = 327/4
To simplify this fraction, we divide the numerator by the denominator:
327 ÷ 4 = 81 remainder 3
So the total length of wood Ted needs for all three picture frames is 81 3/4 inches.
Therefore, the correct answer is option d) 81 3/4 in.