The scale drawing of a room is drawn on a grid that represents a quarter-inch grid paper. The scale is 1/4 in.:4 ft. Redraw the scale drawing of the same room using a different scale. What scale did you use? What is the length and width of the actual room? What is the area of the actual room?
To redraw the scale drawing of the room using a different scale, we need to determine the new scale and then calculate the length and width of the actual room.
Given:
Scale of the original drawing: 1/4 in.:4 ft
To find the new scale, we can set up a proportion using the original scale and the desired scale.
The original scale can be written as:
1/4 in. : 4 ft.
Let's say the new scale is x in. : y ft.
Setting up the proportion, we get:
1/4 in. / 4 ft. = x in. / y ft.
Cross-multiplying gives us:
(1/4) * y ft. = (4/1) * x in.
Simplifying the equation, we have:
y/4 = 4x/1
y = (16/4) * x
y = 4x
Therefore, the new scale is:
x in. : 4x ft.
To find the length and width of the actual room, we can use the measurement on the scale drawing.
Based on the original scale, each quarter-inch on the drawing represents 4 ft in reality. Let's assume the length on the drawing is l inches and the width is w inches.
The length of the actual room can be calculated as:
Length = l inches * 4 ft/inch
The width of the actual room can be calculated as:
Width = w inches * 4 ft/inch
Finally, to find the area of the actual room, we multiply the length by the width:
Area = Length * Width = (l inches * 4 ft/inch) * (w inches * 4 ft/inch) = 16 * l * w square feet.
Therefore, to answer your question, the new scale used is x in. : 4x ft, the length and width of the actual room are l inches * 4 ft/inch and w inches * 4 ft/inch respectively, and the area of the actual room is 16 * l * w square feet.