The length of a rectangle is 5 meters less than twice the width. If the area of the rectangle is 493 square m The width is \( \square \) meters. The length is \( \square \) meters.

Let's denote the width of the rectangle as \( w \) meters. Given that the length of the rectangle is 5 meters less than twice the width, we can express the length as \( 2w - 5 \) meters. The area of a rectangle is given by the formula: Area = Length * Width. We are given that the area of the rectangle is 493 square meters. Therefore, we can set up the equation: \[ (2w - 5) \times w = 493 \] Now, we need to solve this equation to find the value of \( w \), which represents the width of the rectangle. Let's solve the equation step by step. Solve the quadratic equation by following steps: - step0: Solve by factoring: \(\left(2w-5\right)w=493\) - step1: Multiply the terms: \(w\left(2w-5\right)=493\) - step2: Expand the expression: \(2w^{2}-5w=493\) - step3: Move the expression to the left side: \(2w^{2}-5w-493=0\) - step4: Factor the expression: \(\left(w-17\right)\left(2w+29\right)=0\) - step5: Separate into possible cases: \(\begin{align}&w-17=0\\&2w+29=0\end{align}\) - step6: Solve the equation: \(\begin{align}&w=17\\&w=-\frac{29}{2}\end{align}\) - step7: Rewrite: \(w_{1}=-\frac{29}{2},w_{2}=17\) The solutions to the equation are \( w = -\frac{29}{2} \) and \( w = 17 \). Since the width of a rectangle cannot be negative, we discard the solution \( w = -\frac{29}{2} \). Therefore, the width of the rectangle is 17 meters. Now, we can find the length of the rectangle by substituting the value of \( w \) into the expression for the length: Length = \( 2w - 5 \) Substitute \( w = 17 \) into the expression: Length = \( 2(17) - 5 \) Length = \( 34 - 5 \) Length = 29 meters Therefore, the length of the rectangle is 29 meters.