Cynthia is hanging a picture on the wall. The picture is 30 inches wide and 34 inches high and will be hung on a wall that is 10 feet high. The center of the picture must be 6 1/3 feet from the floor. Determine the distance from the ceiling to the top of the picture frame. Explain how you found your answer.I am having difficulty with this.
Thanks!
A picture is worth a thousand words, (groan)
Draw a vertical line and mark it 120 inches
the centre must be 76 inches from the floor or 44 inches from the ceiling.
Since the picture is 34 inches high and you want its centre, just add half of 34 or 17 inches to 76.
So the top of the picture must be 44-17 inches
or 27 inches from the ceiling, (and 59 inches from the floor)
Notice the width of the picture does not enter into the discussion.
check:
floor to bottom of picture + length of picture + top of picture to ceiling
= 59 + 34 + 27 = 120
To determine the distance from the ceiling to the top of the picture frame, we need to subtract the distance from the floor to the center of the picture frame from the total height of the wall.
Given:
Width of the picture (W) = 30 inches
Height of the picture (H) = 34 inches
Height of the wall (HW) = 10 feet
Distance from the floor to the center of the picture frame (DF) = 6 1/3 feet
Convert the height of the wall from feet to inches:
HW = 10 feet * 12 inches = 120 inches
Convert the distance from the floor to the center of the picture frame from feet to inches:
DF = 6 1/3 feet * 12 inches = 76 inches
To determine the distance from the ceiling to the top of the picture frame, subtract the distance from the floor to the center of the picture frame from the total height of the wall:
Ceiling to top of the picture frame = HW - DF
Substituting the given values:
Ceiling to top of the picture frame = 120 inches - 76 inches
Calculating:
Ceiling to top of the picture frame = 44 inches
Therefore, the distance from the ceiling to the top of the picture frame is 44 inches.
To determine the distance from the ceiling to the top of the picture frame, we can follow these steps:
1. Convert the measurements to the same unit. Since the picture's height is given in inches and the wall's height is given in feet, we need to convert the height of the picture from inches to feet.
The height of the picture in feet is 34 inches / 12 inches per foot = 2.83 feet (rounded to two decimal places).
2. Determine the distance from the floor to the center of the picture. We are given that the center of the picture must be 6 1/3 feet from the floor.
Therefore, the distance from the floor to the center of the picture is 6 1/3 feet.
3. Calculate the distance from the floor to the top of the picture frame. To do this, we subtract half of the picture's height from the distance to the center of the picture.
The distance from the floor to the top of the picture frame = (Distance from the floor to the center of the picture) - (Picture's height / 2)
Distance from the floor to the top of the picture frame = 6 1/3 feet - (2.83 feet / 2) = 6.33 feet - 1.42 feet = 4.91 feet (rounded to two decimal places).
4. Finally, we calculate the distance from the ceiling to the top of the picture frame. To do this, we subtract the distance from the floor to the top of the picture frame from the total height of the wall.
Distance from the ceiling to the top of the picture frame = Wall's height - Distance from the floor to the top of the picture frame
Distance from the ceiling to the top of the picture frame = 10 feet - 4.91 feet = 5.09 feet (rounded to two decimal places).
Therefore, the distance from the ceiling to the top of the picture frame is approximately 5.09 feet.