The length of a rectangle is twice its width. if the width is tripled and the length is decreased by 5, the area is increased by 4, find the width. d: --

This one can besolved using system of equations. From the first statement we can assume that length = 2 * width. The area of rectange equals product of it's width and length. By knowing that and following to the second statement we get the second equation: (3 * width) * (length - 5) = width * length + 4. Let's mark the width as x and the length as y and write down our equations system:


Using substituion method, lets replace every y with 2x within second equation and solve it:





Now lets find the discriminant in order to solve this quadratic equation:




The second root is negative, so we ignore it as x represents width which can't be negative.
Now, using found root, let's find y value from the first equation:


So, the width is equal 4 (and the length is equal 8).