Answer :
16 feet. Here's how I got 16: Assuming the room is a rectangle, you would follow these steps: The area of a rectangle is length multiplied by width, or area = length x width. You have the area, so it would be 320 = length x width. We will substitute the length for the variable n. Now your equation looks like this: 320 = n x width. The width is 4/5 of the length, so you would multiply the length, n, by 4/5. width = 4/5n. When you put this in the equation, it would look like this: 320 = n x (4/5n). Next you simplify, so it becomes 320 = 4/5n^2. (^2 means squared.) Then you divide everything by 4/5 to get 400 = n^2. To find n, you find the square root of 400, which gives you 20, so n= 20. Now you know that the length of the room is 20 feet. Since the width is 4/5 the length, you multiply 20 by 4/5 to get 16. The width of the room is 16 feet. If you'd like to check your answer, simply plug the numbers back into the equation and see if they work. 320 = 20 x 16. 20 x 16 does equal 320, so the answer is correct. The width of the room is 16 feet.
