The area of a rectangle mirror is 11 11/16 feet. The width is 2 3/4 feet. If there is a 5 foot tall space on the wall to hang the mirror will it fit explain.
It Will fit.
Divide 11 11/16 by 2 3/4
11.6875 = 2.75L
4.25 = Length
It will fit
whats the height
To determine if the mirror will fit in the given space, we need to compare the area of the mirror to the available wall space.
First, let's calculate the dimensions of the rectangle mirror using the given area and width.
Area of the mirror: 11 11/16 feet
Width: 2 3/4 feet
To find the length of the mirror, we can divide the area by the width:
Length = Area / Width
Length = 11 11/16 feet / 2 3/4 feet
To make this calculation easier, we can convert the mixed numbers to improper fractions:
Length = (11/16 + 11)/4 / (2/4 + 3/4)
Length = (27/16) / (5/4)
When dividing fractions, we can multiply the first fraction by the reciprocal of the second fraction:
Length = (27/16) * (4/5)
Length = (27 * 4) / (16 * 5)
Length = 108 / 80
Length = 27/20
Length = 1 7/20 feet
Now we have the dimensions of the mirror: Width = 2 3/4 feet, Length = 1 7/20 feet.
To determine if the mirror will fit on the wall, we need to compare its height to the available space.
Available space: 5 feet
The height of the mirror is not given, but we can calculate it using the formula for the area of a rectangle:
Area = Length * Width
Substituting the known values:
11 11/16 feet = (1 7/20 feet) * (2 3/4 feet)
Again, let's convert the mixed numbers to improper fractions:
(184/16 + 11)/20 = (8 * 23 + 11)/20 = 195/20
So, the height of the mirror is 195/20 feet.
Now we can compare the height of the mirror (195/20 feet) to the available space (5 feet).
If the height of the mirror is less than or equal to the available space, then the mirror will fit:
195/20 feet <= 5 feet
To make the comparison easier, let's convert both measurements to the same unit. Since both measurements are in feet, we don't need to do any conversion.
Now let's simplify the fraction 195/20:
195/20 = (13 * 15)/(4 * 5) = 13 * 3/4 = 39/4 = 9 3/4
So, the height of the mirror is 9 3/4 feet.
As the height of the mirror (9 3/4 feet) is less than the available space (5 feet), the mirror will fit on the wall with the given dimensions.