Problem

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

Solution

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.

From Solvely APP
Source: https://solvelyapp.com/problems/30937/

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