If the length of molding to create the frame is 96 inches. If the frame surrounding the picture is 3.5 inches wude and the length is 6 inches longer than the width, what are the dimensions (length and width) of the picture that could be placed inside?
To find the dimensions of the picture that could be placed inside the frame, we need to subtract the width of the frame from the length of the molding.
Given:
Length of molding = 96 inches
Width of frame = 3.5 inches
Step 1: Calculate the usable length of the molding by subtracting twice the width of the frame from the total length of the molding.
Usable length of the molding = Length of molding - 2 * Width of frame
Usable length = 96 inches - 2 * 3.5 inches = 96 inches - 7 inches = 89 inches
Step 2: Let's assume the width of the picture is x inches.
According to the given information, the length of the picture is 6 inches longer than the width. Therefore, the length of the picture is x + 6 inches.
Step 3: The dimensions of the picture inside the frame should fit within the usable length of the molding. So we can write the following equation:
Usable length of the molding >= Length of the picture + 2 * Width of the frame
Putting the values in the equation:
89 inches >= (x + 6 inches) + 2 * 3.5 inches
Simplifying the equation:
89 inches >= x + 6 inches + 7 inches
89 inches >= x + 13 inches
Step 4: Solve for x.
Subtracting 13 inches from both sides of the equation:
89 inches - 13 inches >= x
76 inches >= x
Therefore, the width of the picture should be less than or equal to 76 inches.
Step 5: We know that the length of the picture is 6 inches longer than the width. So the length of the picture should be x + 6 inches.
Therefore, the dimensions of the picture that could fit inside the frame are:
Width = x inches (where x is less than or equal to 76 inches)
Length = x + 6 inches (where x is less than or equal to 76 inches)