The length of a rectangle is five times its width. If the perimeter of the rectangle is $84 \mathrm{in}$, find its area.

Step 1 ：Let the width of the rectangle be \(w\) and the length be \(5w\).

Step 2 ：Use the formula for the perimeter of a rectangle: \(P = 2(l + w)\).

Step 3 ：Plug in the given values: \(84 = 2(5w + w)\).

Step 4 ：Solve for \(w\): \(84 = 12w\) which gives \(w = 7\).

Step 5 ：Find the length: \(l = 5w = 5(7) = 35\).

Step 6 ：Find the area using the formula \(A = l * w\): \(A = 35 * 7\).

Step 7 ：\(\boxed{A = 245}\) square inches.