A room measure 12fy by 15ft find the scale that would allow the room to be showed large as possible on a piece of paper 7in by 8in explain your reasoning
To find the scale that would allow the room to be shown as large as possible on a piece of paper, we need to determine the ratio between the dimensions of the room and the dimensions of the paper.
First, let's convert the measurements to the same unit. Since both the room measurements and the paper measurements are given in feet (ft) and inches (in), respectively, let's convert the room measurements to inches:
Room length = 12 ft * 12 in/ft = 144 in
Room width = 15 ft * 12 in/ft = 180 in
Now, we have the dimensions of the room in inches: length = 144 in, width = 180 in.
Next, let's determine the ratio between the dimensions of the room and the dimensions of the paper:
Length ratio = Room length / Paper length = 144 in / 7 in = 20.57
Width ratio = Room width / Paper width = 180 in / 8 in = 22.5
Since we want to find the largest possible representation of the room on the paper, we will need to reduce the room measurements by the same scale factor while still maintaining the room's proportions.
To find the suitable scale factor, we need to find the greatest common divisor (GCD) between the length ratio and the width ratio:
GCD(20.57, 22.5) ≈ 2.5
By dividing both the length ratio and width ratio by the GCD, we obtain:
Length ratio = 20.57 / 2.5 = 8.23
Width ratio = 22.5 / 2.5 = 9
Therefore, the scale that would allow the room to be shown as large as possible on a piece of paper 7 in by 8 in is 1 inch on the paper represents approximately 8.23 inches of the room's length, and 1 inch on the paper represents approximately 9 inches of the room's width.