Question

jillian is trying to save water, so she reduces the size of her square grass lawn by 8 feet on each side. the area of the smaller lawn is 144 square feet. in the equation ((x - 8)^2 = 144), (x) represents the side measure of the original lawn. what were the dimensions of the original lawn?

• 4 feet by 4 feet
• (8 + 6sqrt{2}) feet by (8 + 6sqrt{2})
• (8 - 6sqrt{2}) feet by (8 + 6sqrt{2})
• 20 feet by 20 feet

Explanation:

Step1: Solve the equation \((x - 8)^2 = 144\)

Take the square root of both sides: \(x - 8=\pm\sqrt{144}\)
Since \(\sqrt{144} = 12\), we have \(x - 8=\pm12\)

Step2: Find two cases for \(x\)

Case 1: \(x - 8 = 12\)
Add 8 to both sides: \(x=12 + 8=20\)

Case 2: \(x - 8=- 12\)
Add 8 to both sides: \(x=-12 + 8=-4\)
Since the side length cannot be negative, we discard \(x = - 4\). So the side length of the original square lawn is 20 feet, so the dimensions are 20 feet by 20 feet.

Answer:

D. 20 feet by 20 feet (assuming the last option is D, if the options are labeled as A, B, C, D with the last one being 20 feet by 20 feet)