Your home is on a square lot. To add more space to your yard, you purchase an additional 30 feet along the side of your property (see figure). The area of the lot is now 43,875 square feet. What are the dimensions of the new lot?

A) 180 feet by 210 feet
B) 180 feet by 240 feet
C) 165 feet by 195 feet
D) 195 feet by 225 feet
E) 225 feet by $420$ feet

Question

Your home is on a square lot. To add more space to your yard, you purchase an additional 30 feet along the side of your property (see figure) . The area of the lot is now 43,875 square feet. What are the dimensions of the new lot?

A) 180 feet by 210 feet 
B) 180 feet by 240 feet 
C) 165 feet by 195 feet 
D) 195 feet by 225 feet 
E) 225 feet by $420$ feet

Quizplus · Accepted Answer

Let x be the length of each side of the original square lot. 
The area of the original lot is x^2.

When 30 feet is added to one side, the new length of that side becomes x + 30. 
The area of the new lot is 43,875 square feet.

Thus, we have the equation: 
(x + 30)^2 = 43,875

Simplifying, we get: 
x + 30 = ±sqrt(43,875) 
x + 30 ≈ ±209.2 
x ≈ -30 + 209.2 or x ≈ -30 - 209.2 (we reject the negative solution)

Therefore, x ≈ 179.2

The new dimensions of the lot are (x + 30) by x, which is approximately 209.2 feet by 179.2 feet. 
The closest option is D, which is 195 feet by 225 feet.

Your Home Is on a Square Lot 420420420 Feet

Your Home Is on a Square Lot $420$ Feet