Analyzing Quadratic Word Problems in Housing Contexts

A rectangular garden is to be built next to a house. The length of the garden is 3 meters longer than its width. If the area of the garden is 70 square meters, what are the dimensions of the garden?

• Width: 6 meters, Length: 9 meters

• Width: 7 meters, Length: 10 meters

• Width: 8 meters, Length: 11 meters

• Width: 5 meters, Length: 8 meters

A house is being built with a triangular roof. The height of the roof is 4 meters, and the base is 2 meters longer than the height. What is the area of the roof?

• 8 square meters

• 12 square meters

• 10 square meters

• 15 square meters

The cost of building a house can be modeled by the equation C(x) = x^2 + 50x + 200, where C is the cost in thousands of dollars and x is the number of square meters. How many square meters should be built to minimize the cost?

• 30

• 20

• 40

• 25

A homeowner wants to create a rectangular swimming pool in their backyard. The length is twice the width. If the area of the pool is 128 square meters, what are the dimensions of the pool?

• Width: 10 meters, Length: 20 meters

• Width: 6 meters, Length: 12 meters

• Width: 4 meters, Length: 8 meters

• Width: 8 meters, Length: 16 meters

A construction company finds that the number of houses they can build in a year can be modeled by the equation H(t) = -2t^2 + 12t + 20, where H is the number of houses and t is the number of years. How many houses can they build in 3 years?

• 25

• 38

• 45

• 30

A plot of land is in the shape of a square. If the area of the land is represented by the equation A = x^2, where A is the area in square meters and x is the length of one side, what is the length of each side if the area is 144 square meters?

• 12 meters

• 10 meters

• 14 meters

• 16 meters

A real estate agent sells a house for $300,000. The value of the house can be modeled by the equation V(t) = -5t^2 + 100t + 300, where V is the value in thousands and t is the number of years since it was built. When will the house be worth $200,000?

• Approximately 15.75 years

• Approximately 21.46 years

• Approximately 30.00 years

• Approximately 10.25 years

A family wants to build a new house and has a budget of $250,000. The cost can be modeled by the equation C(x) = 5x^2 + 20x + 100, where C is the cost in thousands and x is the number of rooms. How many rooms can they afford?

• 2

• 8

• 6

• 4

A rectangular lot has a length that is 4 meters longer than its width. If the area of the lot is 96 square meters, what are the dimensions of the lot?

• Width: 5 meters, Length: 9 meters

• Width: 10 meters, Length: 14 meters

• Width: 6 meters, Length: 10 meters

• Width: 8 meters, Length: 12 meters

A city plans to build a new housing development. The number of houses that can be built is represented by the equation N(x) = -x^2 + 10x + 15, where N is the number of houses and x is the number of acres. How many acres should be used to maximize the number of houses?

• 3

• 10

• 7

• 5