The length of a rectangle is five times its width. If the area of the rectangle is \( 180 \mathrm{~m}^{2} \), find its perimeter. \( \square \mathrm{m} \)

Let the width of the rectangle be \( w \). Then the length, \( l \), is \( 5w \). The area of a rectangle is given by the formula \( \text{Area} = \text{length} \times \text{width} \). Therefore, we have the equation: \[ 5w \times w = 180 \] This simplifies to: \[ 5w^2 = 180 \] Dividing both sides by 5 gives: \[ w^2 = 36 \] Taking the square root of both sides, we find: \[ w = 6 \, \text{m} \] Substituting \( w \) back to find the length: \[ l = 5w = 5 \times 6 = 30 \, \text{m} \] Now, we can calculate the perimeter \( P \) of the rectangle using the formula: \[ P = 2(l + w) = 2(30 + 6) = 2 \times 36 = 72 \, \text{m} \] So the perimeter of the rectangle is \( 72 \, \text{m} \).