Question

The area of a rectangle is 14m^2, and the length of the rectangle is 3m less than twice the width. what are the dimensions of the rectangle?

Answer 1

Since the width is the smaller value, make the width=x. That would make the length=2x-3. Area=length*width. Substitute your variables and known values into the equation. 14=(2x-3)(x). Distribute the x to give you $14=2 x^{2} -3x$. Set the equation equal to 0 giving you $2 x^{2} -3x-14=0$. Factor the equation to give you $(2x-7)(x+2)=0$. Set each factor equal to 0 and solve. 2x-7=0 gives you x=7/2 & x+2=0 gives you x=-2. Since we're working with lengths and widths, the answer cannot be negative. Therefore, your width equals 7/2. To find the length, substitute 7/2 into the original expression for length (2x-3). That gives you 2*(7/2)-3=7-3=4. The length is 4.