Question

A scale drawing of a painting is 12 inches long and 8 inches tall. The actual painting is 2 feet tall.

a) What is the scale of the drawing?
b) Find the perimeter and area of the painting in the scale drawing
c) Find the actual perimeter and area of the painting

Answer 1

A)

Scale: 1/3

B)

Permeter: 40 Inches

Area: 96 Square Inches

C)

Perimeter: 120 Inches

Area: 288 Square Inches

Answer 2

Part a)
`4\ (in)/(ft)`

Part b) The perimeter and area of the painting in the scale drawing is 32 inches and 64 square inches respectively

Part c) The perimeter and area of the painting in the scale drawing is 8 feet and 4 square feet respectively

Explanation:

Part a) What is the scale of the drawing?

To find out the scale drawing, divide the corresponding length in the painting by the corresponding length in the actual

so

`(8)/(2)=4\ (in)/(ft)`

That means

4 inches in the drawing represent 1 foot in the actual

Part b) Find the perimeter and area of the painting in the scale drawing

we know that

The length of the painting in the drawing is 8 in

Find the height of the painting in the drawing

Multiply the height of the painting in the actual by the scale drawing

so

`2\ ft=2(4)=8\ in`

Is a square

Find the perimeter

`P=2(8+8)=32\ in`

Find the area

`A=8^2=64\ in^2`

therefore

The perimeter and area of the painting in the scale drawing is 32 inches and 64 square inches respectively

Part c) Find the actual perimeter and area of the painting

we know that

The height of the painting in the actual is 2 ft

Find the length of the painting in the actual

Remember that the figure is a square (see part b)

so

The length of the painting in the actual is 2 ft

Find the perimeter

`P=2(2+2)=8\ ft`

Find the area

`A=2^2=4\ ft^2`

therefore

The perimeter and area of the painting in the scale drawing is 8 feet and 4 square feet respectively