Answer:
Part a) The area of the actual floor is [tex]576\ ft^{2}[/tex]
Part b) The ratio of the area in the drawing to the actual area is [tex]\frac{1}{9}\frac{cm^{2}}{ft^{2}}[/tex]
Step-by-step explanation:
we know that
The scale drawing is [tex]\frac{1}{3}\frac{cm}{ft}[/tex]
step 1
Find the dimensions of the square on a scale drawing
The area of a square is equal to
[tex]A=b^{2}[/tex]
where
b is the length side of the square
[tex]A=64\ cm^{2}[/tex]
so
[tex]64=b^{2}[/tex]
[tex]b=8\ cm[/tex]
step 2
Find the dimensions of the actual floor
Divide the length of the floor on the drawing by the scale drawing
[tex]8/(1/3)=24\ ft[/tex]
step 3
Find the area of the actual floor
The area of a square is equal to
[tex]A=b^{2}[/tex]
substitute
[tex]A=24^{2}=576\ ft^{2}[/tex]
step 4
Find the ratio of the area in the drawing to the actual area
[tex]\frac{64}{576}\frac{cm^{2}}{ft^{2}}[/tex]
Simplify
Divide by 64 both numerator and denominator
[tex]\frac{1}{9}\frac{cm^{2}}{ft^{2}}[/tex]
