# math

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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)?

• math -

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

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