Question

The area of a square for on a scale drawing of 100 square centimeters and the scale drawing to 1 cm: 2 feet what is the area of the actual floor? What is the ratio of the area in the drawing to the actual area

Answer 1

1.
`\boxed{\text{400 ft}^(2)}`; 2.
`\boxed{(1)/(3716)}`

Explanation:

Step 1. Calculate the area of the floor

If the area A₁ of a square floor on the scale drawing is 100 cm², the length of a side is 10 cm.

The side length l of the actual floor is

l = 10 cm × (2 ft/1 cm) = 20 ft

The area A₂ of the floor is

A = l² = (20 ft)² =
`\boxed{\text{400 ft}^(2)}\\`

Step 2. Calculate the area ratios

We must express both areas in the same units.

Let's express the area of the room in square centimetres.

l = 20 ft × (12 in/1 ft) = 240 in

l = 240 in × (2.54 cm/1 in) = 609.6 cm

A₂ = l² = (609.6 cm)² = 371 612 cm²

The area A₁ on the scale drawing is 100 cm².

The ratio of the areas is

`(A_(1))/( A_(2)) = (100)/(371612) = (1 )/(3716)\\`

The ratio of the area in the drawing to the actual area is
`\boxed{(1)/(3716)}`