Answer:
The perimeter of the picture frame is 38.4 in.
The area of the picture frame is 92.6 in.².
Explanation:
The given information are;
Perimeter of side piece of picture frame = 24 inches
Length of side piece = L
Width of side piece = W
Perimeter of side piece = 2 × (L + W) = 24
∴ L + W = 24/2 = 12 inches
Dimension of picture frame = Square frame with side length s
Number of side piece in picture frame = 4
Given that the length L > the width W, we have
Side length of wooden frame = L
Also, where the side piece are placed side by side, we have;
Side length of wooden frame = 4 × W
Therefore;
4 × W = L
Which gives
L + W = 12 inches
4 × W + W = 12 inches
W×(4 + 1) = 5·W = 12 inches
W = 12/5 = 2.4 inches
L = 4 × W = 4 × 12/5
L = 48/5 = 9.6 inches Side length of wooden frame, s
The perimeter of the picture frame = 4 × s = 4 × 9.6 = 38.4 in.
The area of the picture frame = s × s = 9.6 × 9.6 = 92.6 in.².