Question

The length of a rectangular sheet of metal decreases by 34.5 cm. Its width decreases proportionally. If the sheets original width was half the original length and the new area of the sheet is 1.2 m^2 what is the sheets original width and what percent did the area of the sheet change.

Answer 1

The original width was 94.71 cm 
The area decreased 33.1% 

The equation for the final size is 
2X^2 = 1.2 m^2 
X^2 - 0.6 m^2 
X^2 = 10000 * .6 cm 
X = 77.46 cm (this is the width) 

The length is 2 * 77.46 = 154.92 cm 

The original length was 154.92 + 34.5 = 189.42 cm 
The original width was 189.42 / 2 = 94.71 cm 

The original area was 94.71 * 189.92 = 17939.9 cm^2 
The new area is 79.46 * 154.92 = 12000.1 cm^2 

The difference between the original and current area is 17939.9 - 12000.1 = 5939.86 cm^2 

The percentage the area decreased is 5939.86 ' 17939.9 = 33.1%