Question

Length and width from area question below
Area of rectangle 168 feet length ten feet longer than twice the width.

Answer 1

You can form two equations from the information provided. Since area is length*width we have\[168=lw\] and it tells us that the length is ten feet longer than twice the width. So that means if we add 10 to 2w, it will be equal to the length.\[l=2w+10\] You can substitute 2w+10 for l in the area equation to get\[168=w(2w+10)\] Distributing w we get\[168=2w^2+10w\] You can subtract 168 from both sides to get a quadratic equation in the for ax^2+bx+c=0\[2w^2+10w-168=0\] Dividing each term on both sides by 2 we get\[w^2+5w-84=0\] This factors into\[(w+12)(w-7)=0\] Solving for x, we get two possible solutions\[w=-12, w=7\] Because we are dealing with length, the negative solution can be discarded. We can substitute 7 for w in the area equation to solve for l.\[7l=168\]\[l=24\] so the dimensions are w=7 and l=24