Question

The area of a square floor on a scale drawing is 64 square centimeters, and the scale drawing is 1 centimeter:3 ft. What is the area of the actual floor? What is the ratio of the area in the drawing to the actual area? The area of the actual floor is square feet. The ratio of the area in the drawing to the actual area is 1 square centimeter: square feet.

Answer 1

Answer:

Part a) The area of the actual floor is $576\ ft^{2}$

Part b) The ratio of the area in the drawing to the actual area is $\frac{1}{9}\frac{cm^{2}}{ft^{2}}$

Step-by-step explanation:

we know that

The scale drawing is $\frac{1}{3}\frac{cm}{ft}$

step 1

Find the dimensions of the square on a scale drawing

The area of a square is equal to

$A=b^{2}$

where

b is the length side of the square

$A=64\ cm^{2}$

so

$64=b^{2}$

$b=8\ cm$

step 2

Find the dimensions of the actual floor

Divide the length of the floor on the drawing by the scale drawing

$8/(1/3)=24\ ft$

step 3

Find the area of the actual floor

The area of a square is equal to

$A=b^{2}$

substitute

$A=24^{2}=576\ ft^{2}$

step 4

Find the ratio of the area in the drawing to the actual area

$\frac{64}{576}\frac{cm^{2}}{ft^{2}}$

Simplify

Divide by 64 both numerator and denominator

$\frac{1}{9}\frac{cm^{2}}{ft^{2}}$