Question

A homeowner wishes to hang a picture in the middle of a kitchen wall and wants the center of the picture to be exactly 5 3/4 feet up from the floor. The dimensions of the picture and the wall are shown on the attatchment

Which of the following is true about the location of the picture?
The bottom of the picture is 4'9" from the floor.
The top of the picture is 2'3" from the ceiling.
The left side of the picture is 3'8" from the left side of the wall.
The left side of the picture is 7'4" from the left side of the wall.

Answer 1

Explanation:

1+1 is 2

Answer 2

Option C is correct

To determine the location of the picture, we need to calculate the distance from the floor to the bottom of the picture, from the ceiling to the top of the picture, and from the sides of the wall to the sides of the picture. We'll use the dimensions provided:

1. Picture dimensions: 36 inches wide, 28 inches tall.

2. Wall dimensions: 10 feet 4 inches wide, 8 feet tall.

3. Desired center height of the picture from the floor: 5 feet and 3/4 of a foot (which is 9 inches), so 5 feet 9 inches.

Let's calculate:

- The distance from the floor to the bottom of the picture:

The center of the picture is at 5 feet 9 inches, so we need to subtract half the height of the picture to find the height of the bottom from the floor.

`\( 5'9`

- The distance from the ceiling to the top of the picture:

Since the wall is 8 feet high and the center of the picture is at 5 feet 9 inches, the distance from the center of the picture to the ceiling is 2 feet 3 inches. Now, we add half the height of the picture to this to find the distance from the ceiling to the top of the picture.

`\( 2'3`

- The distance from the left side of the wall to the left side of the picture:

To center the picture, we need to divide the leftover horizontal space by 2. The wall is 10 feet 4 inches (or 124 inches) and the picture is 36 inches wide.

`\( (124`

So the left side of the picture is 44 inches (or 3 feet 8 inches) from the left side of the wall.

- The distance from the left side of the wall to the right side of the picture:

Subtracting the distance from the left side of the wall to the left side of the picture from the total width of the wall gives us:

`\( 124`

But since the picture is 36 inches wide, the distance from the left side of the wall to the right side of the picture is actually:

`\( 80`

This means that the left side of the picture is also 44 inches (or 3 feet 8 inches) from the right side of the wall, confirming that it is centered.

Based on these calculations, we can determine which statement about the location of the picture is true. Let's calculate the precise values.

Based on the calculations:

- The bottom of the picture is 4 feet 7 inches from the floor.

- The top of the picture is 1 foot 1 inch from the ceiling.

- The left side of the picture is 3 feet 8 inches from the left side of the wall.

None of the provided statements exactly match the calculated distances. However, the closest correct statement, based on the calculations, is:

"The left side of the picture is 3'8" from the left side of the wall."

This matches our calculation that the picture is centered, with both the left and the right sides being 3 feet 8 inches from their respective sides of the wall.