The length of a rectangle is five times its width. If the perimeter of the rectangle is 84 m, find its area. square m^2

To find the area of the rectangle, we first need to determine the length and width of the rectangle.<br /><br />Let's denote the width of the rectangle as \( w \) meters. Since the length is five times the width, the length can be represented as \( 5w \) meters.<br /><br />The perimeter of a rectangle is given by the formula:<br />\[ P = 2 \times (length + width) \]<br /><br />Given that the perimeter is 84 meters, we can set up the equation:<br />\[ 84 = 2 \times (5w + w) \]<br /><br />Simplifying the equation:<br />\[ 84 = 2 \times 6w \]<br />\[ 84 = 12w \]<br /><br />Now, solve for \( w \):<br />\[ w = \frac{84}{12} \]<br />\[ w = 7 \]<br /><br />So, the width of the rectangle is 7 meters. Now, we can find the length:<br />\[ length = 5w = 5 \times 7 = 35 \]<br /><br />Now that we have the length and width, we can calculate the area of the rectangle using the formula:<br />\[ A = length \times width \]<br />\[ A = 35 \times 7 \]<br />\[ A = 245 \]<br /><br />Therefore, the area of the rectangle is \( 245 \, m^2 \).