Question

Carol has a small Copley of a painting. The dimensions of her copy are shown at the right. The scale of the copy is 0.5 inches: 12 centimeter.

Question A) Find the dimensions of the original painting.

Question B) Find the area of the original painting.

Question C) One centimeter is equal to approximately 0.033 foot. Find the dimensions of the original painting in feet. Round to the nearest thousandth.

Answer 1

(A) 42 cm by 126 cm.

(B) 5,292 square centimeters.

(C) 1.386 feet by 4.158 feet

Explanation:

The scale of the copy is 0.5 : 12, which means 0.5 inches of the copy represents 12 centimeters actual.

From the given scale we can deduct that 1 inch equals 24 centimeters.

So, the dimensions of the original are

`1.75 * 24 =42`

`5.25 * 24= 126`

Therefore, the original painting has dimensions 42 cm by 126 cm. (A)

Notice that the original painting is also rectangular, so its area is

`A_(original)=42 * 126 = 5,292 cm^(2)` (B)

Now, if 1 centimeter is equivalen to 0.033 foot, the dimensions of the original painting in feet are

`42 * 0.033 =1.386 ft\\126 * 0.033=4.158 ft`

Therefore, the dimensions in feet are 1.386 feet by 4.158. (C)

Answer 2

Question A: The dimensions of the original painting are 42 cm by 126 cm.

Question B: The area of the original painting is
`5292cm^2`

Question C: The dimensions of the painting in feet are 1.386 ft by 4.158 ft.

Explanation:

Question A:

The scale of the copy is

0.5 inches:12 centimeter.

This means that 1 inch on the scale is 24 centimeters.

Therefore the width of the original painting is:

`1.75*24cm=42cm`

and the height of is:

`5.25*24cm=126cm`

Therefore the dimension of the original painting are 42 cm by 126 cm.

Question B;

The area of the original painting is just width multiplied by height:

`Area=42cm*126cm=5292cm^2`

Question C:

We convert the dimensions of the painting from centimeters to feet:

`width=42cm*0.033(feet)/(cm) =1.386\:feet.`

`height=126cm*0.033(feet)/(cm) =4.158\:feet.`

Therefore the dimensions of the original painting in feet are 1.386 ft by 4.158 ft.