A rectangular poster has an area of 38 square feet. It is 4 3/4
feet wide at its base. What is the height of the poster?
Can someone walk me through how to get the answer? I can figure out a rectangle, until they throw in a fraction.
Thank you!
L= length
W = width = 4 3 / 4 = 4 + 3 / 4 = 16 / 4 + 3 / 4 = 19 / 4 ft
A = Area = 38 ft²
A = L ∙ W
38 = L ∙ 19 / 4
Divide both sides by 19
2 = L / 4
Multiply both sides by 4
8 = L
L = 8 ft
Check of result.
W = width = 4 3 / 4 = 4 + 3 / 4 = 4.75 ft
A = L ∙ W = 8 ft ∙ 4.75 ft = 38 ft²
To find the height of the rectangular poster, we need to divide the area by the width of the base.
The area of the poster is given as 38 square feet.
The width of the base is 4 3/4 feet.
To solve this:
Step 1: Convert the mixed number 4 3/4 to an improper fraction.
- Multiply the whole number (4) by the denominator of the fraction (4) and add the numerator (3).
- This will give us (4*4) + 3 = 19.
- The improper fraction is 19/4.
Step 2: Divide the area by the width to find the height.
- To divide fractions, we multiply the first fraction (area) by the reciprocal of the second fraction (width).
- The reciprocal of 19/4 is 4/19.
So, the height of the poster is calculated as 38/ (19/4) which is the same as 38 * (4/19).
- Multiply the numerator and denominator: 38 * 4 = 152.
- The height of the poster is 152/19 feet.
Therefore, the height of the rectangular poster is 8 feet.
To find the height of the rectangular poster, we need to use the formula for the area of a rectangle: Area = Width x Height.
In this case, the given area is 38 square feet. The width is given as 4 3/4 feet.
To work with the fraction, we need to convert it to a decimal or improper fraction.
To convert the mixed number 4 3/4 to an improper fraction, we follow these steps:
1. Multiply the whole number (4) by the denominator (4): 4 x 4 = 16.
2. Add the product to the numerator (3): 16 + 3 = 19.
3. Write the sum (19) over the denominator (4), and put it in the form of an improper fraction: 19/4.
So, the width of the poster is 4 3/4 feet, which is equivalent to 19/4 feet.
Now, we can substitute the known values into the formula and solve for the height:
Area = Width x Height
38 = 19/4 x Height
To find the height, we can isolate the variable by multiplying both sides of the equation by the reciprocal of 19/4, which is 4/19:
(4/19) x 38 = (4/19) x (19/4) x Height
152/19 = Height
Therefore, the height of the poster is 152/19 feet.
If you prefer a decimal answer, you can calculate the division:
Height ≈ 7.368 feet (rounded to three decimal places).