math
posted by pitigoiu .
A rectangular room has an area of 120ft squared. Marge drew a scale drawing of the pool using the scale 1.5cm=2ft. What was the area of the scale drawing?
a) 213.3cm2
b) 67.5cm2
c)53.3cm2
d)1.5cm2
I don't think any of the choices match the answer (90cm2)?

After the scaling, the new shape is similar to the old shape
areas of similar shapes are proportional to the square of their sides
120 ft^2/2^2 = A/1.5^2
120/4 = A/2.25
A = 120(2.25)/4 = 67.5
OR
suppose the actual room was 10 ft by 12 ft > area = 120 ft^2
in our scale the room would be 7.5 cm by 9 cm
area of scaled room = 7.5(9) or 67.5 cm^2