Identify the perimeter of a rectangle in which \( h=9 \mathrm{ft} \) and \( A=225 x \mathrm{ft}^{2} \). \( P=(18+50 x) \mathrm{ft} \) \( P=(9+25 x) \mathrm{ft} \) \( P=(9 x+25) \mathrm{ft} \) \( P=(18 x+50) \mathrm{ft} \)

To find the perimeter, we first need to determine the width \( w \) of the rectangle using the area formula \( A = h \times w \). Given \( A = 225x \) and \( h = 9 \) ft, we can set up the equation: \[ 225x = 9w \] Solving for \( w \): \[ w = \frac{225x}{9} = 25x \text{ ft} \] Now, we can calculate the perimeter \( P \) of the rectangle using the formula \( P = 2(h + w) \): \[ P = 2(9 + 25x) = 18 + 50x \text{ ft} \] Thus, the correct answer for the perimeter is \( P = (18 + 50x) \mathrm{ft} \). Now, let's take a look at some additional insights: Understanding the historical evolution of geometry can make math feel like a thrilling adventure! Ancient civilizations, from the Egyptians to the Greeks, made significant contributions to geometry. Like the Greeks, whose famous mathematician Euclid formalized the study of geometry in his work "Elements," they laid the groundwork for calculating areas and perimeters. So, every time you calculate the perimeter of a rectangle, you’re tapping into thousands of years of mathematical discovery! If you're tackling problems like this often, one common mistake is neglecting to double-check your area and dimension units. Ensure that when you're working with areas (like \( ft^2 \)) and linear measurements (like \( ft \)), everything is consistent. Always remember that the perimeter formula involves summing lengths, so clarity in dimensions helps avoid any sticky situations!