Factoring Quadratics: Real-Life Problem Solving for 9th Graders

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 40 square meters, what are the dimensions of the garden?

• Width: 4 meters, Length: 7 meters

• Width: 5 meters, Length: 8 meters

• Width: 6 meters, Length: 9 meters

• Width: 3 meters, Length: 6 meters

A ball is thrown upwards from a height of 5 meters with an initial velocity of 10 meters per second. The height of the ball in meters after t seconds is given by the equation h(t) = -5t^2 + 10t + 5. When will the ball hit the ground?

• 1.5 seconds

• 3.0 seconds

• Approximately 2.414 seconds

• 4.2 seconds

The product of two consecutive integers is 72. What are the integers?

• 7 and 8

• 9 and 10

• 8 and 9

• 6 and 7

A rectangular pool has a length that is twice its width. If the area of the pool is 200 square meters, what are the dimensions of the pool?

• Width: 8 meters, Length: 16 meters

• Width: 15 meters, Length: 30 meters

• Width: 5 meters, Length: 10 meters

• Width: 10 meters, Length: 20 meters

A farmer has a rectangular field. The length is 4 meters less than twice the width. If the area of the field is 48 square meters, what are the dimensions of the field?

• Width: 4 meters, Length: 10 meters

• Width: 5 meters, Length: 7 meters

• Width: 8 meters, Length: 8 meters

• Width: 6 meters, Length: 8 meters

The difference between the squares of two consecutive integers is 1. What are the integers?

• 1 and 2

• 0 and 1

• 2 and 3

• -1 and 0

A triangle has a base that is 2 meters longer than its height. If the area of the triangle is 24 square meters, what are the dimensions of the triangle?

• Height: 4 meters, Base: 6 meters

• Height: 5 meters, Base: 7 meters

• Height: 8 meters, Base: 10 meters

• Height: 6 meters, Base: 8 meters

A car's value decreases according to the equation V(t) = -200t^2 + 4000, where V is the value in dollars and t is the time in years. When will the car's value reach zero?

• 4.47 years

• 5.0 years

• 2.5 years

• 3.2 years

The length of a rectangular piece of land is 5 meters more than its width. If the area of the land is 60 square meters, what are the dimensions of the land?

• Length: 12 meters, Width: 6 meters

• Length: 15 meters, Width: 10 meters

• Length: 8 meters, Width: 3 meters

• Length: 10 meters, Width: 5 meters

A rectangular box has a length that is 3 meters longer than its width. If the volume of the box is 60 cubic meters and the height is 2 meters, what are the dimensions of the box?

• Width: 5 meters, Length: 10 meters, Height: 3 meters

• Width: 4 meters, Length: 7 meters, Height: 2 meters

• Width: 6 meters, Length: 9 meters, Height: 2 meters

• Width: 5 meters, Length: 8 meters, Height: 2 meters