Question

MONA LISA A visitor to the Louvre Museum in Paris wants to sketch a drawing of the Mona Lisa, a famous painting. The original painting is 77 centimeters by 53 centimeters. Choose an appropriate scale for the replica so that it will fit on a 8.5-by-11-inch sheet of paper.

Answer 1

To scale the replica of the Mona Lisa to fit on an 8.5-by-11-inch sheet of paper, we calculate the scale factor by finding the ratio between the dimensions of the original painting and the dimensions of the paper. We then multiply the scale factor by the dimensions of the original painting to find the dimensions of the replica.

Step-by-step explanation:

To determine an appropriate scale for the replica of the Mona Lisa so that it will fit on an 8.5-by-11-inch sheet of paper, we need to find the ratio between the dimensions of the original painting and the dimensions of the paper.

The ratio of the width of the original painting to the width of the paper is 77 cm / 21 inches, and the ratio of the height of the original painting to the height of the paper is 53 cm / 30.25 inches.

Now, we need to find the scale factor that will allow the replica to fit on the paper. We can do this by finding the smaller ratio between the two ratios calculated above. In this case, the smaller ratio is the ratio of the height. So, the scale factor is 11 inches / 30.25 inches.

To find the dimensions of the replica, we can multiply the scale factor by the dimensions of the original painting. The width of the replica is 21 inches * (11 inches / 30.25 inches) = 7.6169 inches (rounded to the nearest hundredth) and the height of the replica is 30.25 inches * (11 inches / 30.25 inches) = 11 inches.

Answer 2

You need to find a scale factor of dilation (probably contraction) to make the replica.

Given that the units of the original painting are centimeters and the units of the sheet of paper are in inches, you have to convert one of the units.

I choose to covert inches to centimeters.

To do that, use the conversion factor 1 = 2.54 cm / inch

=> 8.5 in * [2.54 cm/in] = 21.59 cm

=> 11 in * [2.54 cm/in] = 27.94 cm

Now determine the scale factor to convert 77 cm to 27.94 cm and 53 cm to 21.59 cm. That just require use of division operation:

77 / 27.94 = 2.76

53 / 21.59 = 2.45

Then the higher scale factor is the relevant one, and you have to reduce the original painting by a factor of (1 / 2.76) which will lead to fit in the sheet of paper.