Factoring Real-Life Problems: Quadratics in Action

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: 3 meters, Length: 6 meters

• Width: 4 meters, Length: 7 meters

• Width: 5 meters, Length: 8 meters

• Width: 6 meters, Length: 9 meters

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

• 6 and 7

• 9 and 10

• 7 and 8

• 8 and 9

A ball is thrown upwards from a height of 5 meters. The height of the ball in meters after t seconds is given by the equation h(t) = -5t^2 + 20t + 5. When will the ball hit the ground?

• 2.75 seconds

• 5.0 seconds

• 3.5 seconds

• 4.24 seconds

The area of a triangle is 24 square meters. If the base is 2 meters longer than the height, find the base and height of the triangle.

• Base: 10 meters, Height: 4 meters

• Base: 5 meters, Height: 5 meters

• Base: 12 meters, Height: 2 meters

• Base: 8 meters, Height: 6 meters

A rectangular pool has a length that is twice its width. If the area of the pool is 100 square meters, what are the dimensions of the pool?

• Width: 8 meters, Length: 16 meters

• Width: 6 meters, Length: 12 meters

• Width: 5 meters, Length: 10 meters

• Width: 7.07 meters, Length: 14.14 meters

The difference between the squares of two numbers is 45. If one number is 5 more than the other, find the two numbers.

• 25 and 20

• 20 and 15

• 15 and 10

• 12 and 7

A car's value decreases according to the equation V(t) = -200t^2 + 5000, where V is the value in dollars and t is the time in years. When will the car's value be zero?

• 5 years

• 7 years

• 3 years

• 10 years

The length of a rectangle is 4 meters less than twice its width. If the area of the rectangle is 32 square meters, what are the dimensions of the rectangle?

• Width: 4 meters, Length: 8 meters

• Width: 3 meters, Length: 10 meters

• Width: 5 meters, Length: 6 meters

• Width: 6 meters, Length: 4 meters

A farmer has a rectangular field. The length is 10 meters more than the width, and the area is 200 square meters. What are the dimensions of the field?

• Width: 5 meters, Length: 15 meters

• Width: 12 meters, Length: 22 meters

• Width: 10 meters, Length: 20 meters

• Width: 15 meters, Length: 25 meters

The sum of the squares of two numbers is 85, and their product is 24. What are the two numbers?

• 6 and 4

• 10 and 5

• The two numbers are 9 and 2.

• 7 and 3