The length of a rectangular sheet of metal decreases by 34.5 cm. Its width decreases proportionally. If the sheets original widt
h 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.
The original width was 94.71 cm <span>The area decreased 33.1% </span>
<span>The equation for the final size is </span> <span>2X^2 = 1.2 m^2 </span> <span>X^2 - 0.6 m^2 </span> <span>X^2 = 10000 * .6 cm </span> <span>X = 77.46 cm (this is the width) </span>
<span>The length is 2 * 77.46 = 154.92 cm </span>
<span>The original length was 154.92 + 34.5 = 189.42 cm </span> <span>The original width was 189.42 / 2 = 94.71 cm </span>
<span>The original area was 94.71 * 189.92 = 17939.9 cm^2 </span> <span>The new area is 79.46 * 154.92 = 12000.1 cm^2 </span>
<span>The difference between the original and current area is 17939.9 - 12000.1 = 5939.86 cm^2 </span>
<span>The percentage the area decreased is 5939.86 ' 17939.9 = 33.1%</span>
