SOLUTION: a rectangular room has an area of 60 ft^2.the width is 4 feet less than its length.find the width of the room.you don't have to draw a diagram. thanks.

Algebra ->  Trigonometry-basics -> SOLUTION: a rectangular room has an area of 60 ft^2.the width is 4 feet less than its length.find the width of the room.you don't have to draw a diagram. thanks.      Log On


   

Question 621041: a rectangular room has an area of 60 ft^2.the width is 4 feet less than its length.find the width of the room.you don't have to draw a diagram. thanks.
Answer by matt501823(7) About Me  (Show Source):
You can put this solution on YOUR website!
You know that the surface area must be 60+ft%5E2. You also know that length times width equals the area, A. Thus you can say that L%2AW=60, but you can also substitute in an alternate value for W since you know that width is 4 less than the length. Thus, we can now say L%2A%28L-4%29=60 this is the same as saying L%5E2-4L=60 (this was achieved by factoring). Now you can also say L%5E2-4L-60=0. We can now factor this expression and can determine that %28L-10%29%2A%28L%2B6%29=0. This means that either L-10=0 or that L%2B6=0. If we solve for L-10=0 you get L=10; however if you solve for L+6=0 you get L=-6. Since you cannot have a negative length value the length must be 10 feet. Thus we can determine that the width must be 6 feet as 10-4=6. Now, let's double-check to make sure that our length and width values result in a surface area of 60+ft%5E2:
10%2A6=60
60=60
It works :)