Solving Real-Life Quadratics: Word Problems & Roots

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: 6 meters, Length: 9 meters

• Width: 5 meters, Length: 8 meters

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

• 9 and 10

• 7 and 8

• 8 and 9

• 6 and 7

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. When will the ball hit the ground?

• 3.0 seconds

• Approximately 2.414 seconds

• 1.5 seconds

• 4.2 seconds

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: 15 meters, Length: 30 meters

• Width: 5 meters, Length: 10 meters

• Width: 8 meters, Length: 16 meters

• Width: 10 meters, Length: 20 meters

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

• 2 and 3

• 0 and 1

• 1 and 2

• -1 and 0

A company produces a certain product and finds that the profit, P, in dollars, can be modeled by the equation P(x) = -x^2 + 12x - 20, where x is the number of units sold. How many units must be sold to break even?

• 1 or 3

• 5 or 7

• 2 or 10

• 4 or 6

The area of a triangular plot of land is 60 square meters. If the base is 4 meters longer than the height, what are the dimensions of the base and height?

• Base: 12 meters, Height: 8 meters

• Base: 14 meters, Height: 10 meters

• Base: 16 meters, Height: 12 meters

• Base: 10 meters, Height: 6 meters

A rectangular box has a volume of 120 cubic centimeters. If the length is 2 centimeters longer than the width and the height is 3 centimeters, what are the dimensions of the box?

• Width: 4 cm, Length: 6 cm, Height: 3 cm

• Width: 10 cm, Length: 12 cm, Height: 3 cm

• Width: 6 cm, Length: 8 cm, Height: 3 cm

• Width: 5 cm, Length: 7 cm, Height: 3 cm

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

• 7 and 3

• 10 and 5

• 6 and 4

• The two numbers are 9 and 2.

A farmer has a rectangular field where the length is 5 meters more than twice the width. If the area of the field is 100 square meters, what are the dimensions of the field?

• Length: 12 meters, Width: 6 meters

• Length: 10 meters, Width: 10 meters

• Length: 15 meters, Width: 5 meters

• Length: 20 meters, Width: 5 meters