Final answer:
To find the length of side x, we can set up a proportion: 0.5 inch/20 miles = 8 inches/x miles. Cross-multiplying and solving for x gives us x = 320 miles.
Step-by-step explanation:
The given information provides a ratio representing the length of the side. We have 0.5 inch/20 miles = 8 inches/x miles. To find the length of side x, we can set up a proportion: 0.5 inch/20 miles = 8 inches/x miles. Cross-multiplying and solving for x gives us x = (20*8 inches)/(0.5 inch) = <<20*8/0.5=320>>320 miles.
To find the length of side x, mathematical principles like ratios and the Pythagorean theorem are utilized. For example, a scale to actual length ratio is set up such that 0.5 inch/20 miles equals 8 inches/x miles. Following the setup, the variable x is isolated through cross-multiplication, resulting in a straightforward algebraic equation to find its value.
If we are given a scenario where the dimensions of a square are increased by a scale factor, we simply multiply the original dimension by the scale factor to find the new length. When working with scales for wingspans, maps, or any other dimensional representation, it is essential to maintain the correct ratio to find the actual length. This concept is also fundamental in solving problems related to right triangles using the Pythagorean theorem, where side lengths are calculated to find the hypotenuse or one of the legs.