Factoring and Solving Quadratics in Real-Life Scenarios

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: 3 meters, Length: 6 meters

• Width: 6 meters, Length: 9 meters

A school is planning to build a new playground. The area of the playground is represented by the polynomial x^2 - 5x + 6. Factor this polynomial to find the possible dimensions of the playground.

• (x - 4) and (x - 5)

• (x + 2) and (x + 3)

• The possible dimensions of the playground are (x - 2) and (x - 3).

• (x - 1) and (x - 6)

A farmer has a rectangular field. The length of the field is twice its width. If the area of the field is 72 square meters, what are the dimensions of the field?

• Width: 6 meters, Length: 12 meters

• Width: 3 meters, Length: 6 meters

• Width: 5 meters, Length: 10 meters

• Width: 4 meters, Length: 8 meters

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

• 8 and 9

• 9 and 10

• 6 and 7

• 7 and 8

A rectangular pool has a length that is 4 meters longer than its width. If the area of the pool is 60 square meters, find the dimensions of the pool by factoring the quadratic equation.

• Width: 7 meters, Length: 11 meters

• Width: 6 meters, Length: 10 meters

• Width: 8 meters, Length: 12 meters

• Width: 5 meters, Length: 9 meters

A box has a volume of 120 cubic centimeters. If the height of the box is 5 cm and the length is 2 cm more than the width, find the dimensions of the box by solving the polynomial equation.

• Width: 4 cm, Length: 6 cm, Height: 5 cm

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

• Width: 4 cm, Length: 8 cm, Height: 5 cm

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

The area of a triangular garden is represented by the equation A = 1/2 * base * height. If the base is 3 meters longer than the height and the area is 36 square meters, find the dimensions of the garden.

• Height: 4 meters, Base: 7 meters

• Height: 5 meters, Base: 8 meters

• Height: 7 meters, Base: 10 meters

• Height: 6 meters, Base: 9 meters

A rectangle's length is 5 meters more than its width. If the perimeter of the rectangle is 50 meters, find the dimensions of the rectangle by solving the quadratic equation.

• Width: 8 meters, Length: 13 meters

• Width: 5 meters, Length: 10 meters

• Width: 10 meters, Length: 15 meters

• Width: 12 meters, Length: 17 meters

A rectangular plot of land has an area of 144 square meters. If the length is 12 meters, what is the width of the plot?

• 12 meters

• 16 meters

• 14 meters

• 10 meters

A rectangular room has a length that is 2 meters longer than its width. If the area of the room is 48 square meters, find the dimensions of the room by factoring the quadratic equation.

• Width: 4 meters, Length: 6 meters

• Width: 5 meters, Length: 7 meters

• Width: 7 meters, Length: 9 meters

• Width: 6 meters, Length: 8 meters