Solving Quadratics: Housing and Area Challenges

A rectangular garden is to be built with a length that is 3 meters longer than its width. If the area of the garden is 70 square meters, what are the dimensions of the garden? Solve the quadratic equation to find the width and length.

• Width: 5 meters, Length: 8 meters

• Width: 6 meters, Length: 9 meters

• Width: 8 meters, Length: 11 meters

• Width: 7 meters, Length: 10 meters

A house is being built with a roof that forms a parabolic shape. The height of the roof can be modeled by the equation h(x) = -2x^2 + 8x, where h is the height in meters and x is the distance from the center of the roof. What is the maximum height of the roof?

• 4 meters

• 10 meters

• 8 meters

• 6 meters

The cost of building a house can be modeled by the equation C(x) = 3x^2 + 12x + 5, where C is the cost in thousands of dollars and x is the number of rooms. How many rooms should be built to minimize the cost?

• 3

• 0

• 1

• 2

A homeowner wants to create a rectangular swimming pool in their backyard. The length of the pool is 4 meters longer than its width. If the area of the pool is 96 square meters, what are the dimensions of the pool?

• Width: 6 meters, Length: 10 meters

• Width: 5 meters, Length: 9 meters

• Width: 8 meters, Length: 12 meters

• Width: 10 meters, Length: 14 meters

The height of a projectile launched from a house can be modeled by the equation h(t) = -5t^2 + 20t + 15, where h is the height in meters and t is the time in seconds. When will the projectile hit the ground?

• 4.00 seconds

• 5.25 seconds

• 3.47 seconds

• 2.15 seconds

A triangular plot of land has a base that is 2 meters longer than its height. If the area of the plot is 50 square meters, what are the dimensions of the plot?

• Height: 10 meters, Base: 12 meters

• Height: 6 meters, Base: 8 meters

• Height: 5 meters, Base: 7 meters

• Height: 8 meters, Base: 10 meters

A construction company is designing a new house. The area of the living room can be represented by the equation A(x) = x^2 + 6x, where A is the area in square meters and x is the length of one side. What is the area of the living room when the side length is 4 meters?

• 30 square meters

• 50 square meters

• 24 square meters

• 40 square meters

A rectangular house has a length that is twice its width. If the perimeter of the house is 60 meters, what are the dimensions of the house?

• Length: 30 meters, Width: 15 meters

• Length: 25 meters, Width: 12.5 meters

• Length: 15 meters, Width: 7.5 meters

• Length: 20 meters, Width: 10 meters

The path of a ball thrown from a window can be modeled by the equation h(t) = -4.9t^2 + 20t + 30. How long will it take for the ball to reach the ground?

• 3 seconds

• 7 seconds

• 10 seconds

• 5 seconds

A homeowner wants to build a fence around a rectangular garden. The length of the garden is 5 meters longer than its width. If the total area of the garden is 50 square meters, what are the dimensions of the garden?

• Width: 5 meters, Length: 8 meters

• Width: 6 meters, Length: 11 meters

• Width: 5 meters, Length: 10 meters

• Width: 4 meters, Length: 9 meters