a scale drawing for a new city library shows a rectangular children's reading room with a length of 5 1/4 inches and a width of 3 1/2 inches. The scale on the is 1 inch:4feet . What will be the actual length and with of the room when the library is built.
Can someone explain how to do this.
5.25 * 4 = 21 feet
3.5 * 4 = 14 feet
Thank You
You're welcome.
To determine the actual length and width of the children's reading room in the library, you need to convert the measurements from the scale drawing to their real-world values.
Given:
Length of the reading room in the scale drawing = 5 1/4 inches
Width of the reading room in the scale drawing = 3 1/2 inches
Scale on the drawing = 1 inch:4 feet
To start, select either the length or the width of the reading room and convert it to its corresponding real-world value. Let's choose the length.
Since the scale is 1 inch:4 feet, this means that 1 inch in the drawing represents 4 feet in reality.
To convert the length of the reading room from inches to feet, multiply it by the conversion factor:
Length in feet = Length in inches x Conversion factor
Length in inches = 5 1/4 inches
To convert the mixed number 5 1/4 into an improper fraction, multiply the whole number (5) by the denominator (4) and add the numerator (1). Then put this total over the original denominator (4).
Length in inches = (5 x 4 + 1) / 4 = 21/4 inches
Now, multiply the length in inches by the conversion factor (1 inch:4 feet) to get the actual length in feet:
Length in feet = (21/4 inches) x (4 feet/1 inch)
Cancel out the inches and simplify:
Length in feet = 21/4 x 4 feet/1
Length in feet = 84/4 feet
Length in feet = 21 feet
So, according to the scale drawing, the length of the children's reading room is 5 1/4 inches, but the actual length when the library is built will be 21 feet.
Similarly, you can follow the same steps to find the actual width of the reading room. Given that the width of the reading room in the scale drawing is 3 1/2 inches, you can convert it to its real-world value by multiplying by the conversion factor (1 inch:4 feet).