Factoring Quadratics: Real-Life Applications in Geometry

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: 6 meters, Length: 9 meters

• Width: 3 meters, Length: 6 meters

• Width: 5 meters, Length: 8 meters

• Width: 4 meters, Length: 7 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 after t seconds is given by the equation h(t) = -5t^2 + 10t + 5. Factor this equation to find the times when the ball hits the ground.

• t = 1 ± √4

• t = 1 ± √2

• t = 2 ± √3

• t = 0 ± √5

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

• 9 and 10

• 6 and 7

• 7 and 8

• 8 and 9

A rectangular pool has a length that is twice its width. If the area of the pool is 200 square meters, find the dimensions of the pool by factoring the quadratic equation.

• 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 96 square meters, find the dimensions of the field by factoring the quadratic expression.

• Width: 8 meters, Length: 12 meters

• Width: 4 meters, Length: 16 meters

• Width: 10 meters, Length: 8 meters

• Width: 6 meters, Length: 10 meters

The area of a triangle is given by the formula A = 1/2 * base * height. If the base is 2 meters longer than the height and the area is 30 square meters, find the base and height by solving the quadratic equation.

• Base: 6 meters, Height: 4 meters

• Base: 8 meters, Height: 6 meters

• Base: 10 meters, Height: 5 meters

• Base: 7 meters, Height: 5 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. Factor this equation to find when the car's value will be zero.

• t = 1.5√5 (approximately 3.35 years)

• t = 5 years

• t = 2√5 (approximately 4.47 years)

• t = 3 years

A rectangular piece of land has a length that is 5 meters more than its width. If the area of the land is 60 square meters, find the dimensions of the land by factoring the quadratic equation.

• Width: 5 meters, Length: 10 meters

• Width: 4 meters, Length: 8 meters

• Width: 6 meters, Length: 9 meters

• Width: 7 meters, Length: 12 meters

The height of a projectile is modeled by the equation h(t) = -16t^2 + 32t + 48. Factor this equation to determine when the projectile reaches the ground.

• t = 1

• t = 3

• t = 2

• t = 4

A rectangular box has a volume of 120 cubic centimeters. If the length is 3 centimeters more than the width and the height is 2 centimeters, find the dimensions of the box by factoring the quadratic expression.

• Width: 4 cm, Length: 7 cm, Height: 3 cm

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

• Width: 5 cm, Length: 10 cm, Height: 1 cm

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