The length of a rectangle is five less than three times the width. If the area of the rectangle is 112 square feet, what are the dimensions of the rectangle?

Answer 1

In order to solve this problem you will need to use X as a variable for the length and the width. If we are assuming x is the width, then we can find the length by taking 3x-5 (since it is five less than three times the width of x). To find the area of a rectangle, you are multiplying the length and width or x (3x-5) which gives us 3x²-5x. We also know the area is the same as 112 ft² so if we set them equal to each other we can solve for x. The best way to solve for x would be to set one side of the equation equal to zero, or 3x²-5x-112=0 and then factor. There are many ways to factor but you should end up with (x-7)(3x+16)=0 Your final step involves solving for x, which gives you 7 and -16/3. If you think about the original question, it wouldn't make sense to have a width of negative anything, so -16/3 is not used. To answer the question you take x=7 and plug it back in for your width and length. Width=7, Length is 3(7)-5 or 16. Final answer: Width is 7 ft, length is 16 ft