Quadratics in Action: Area, Perimeter, and Graphing

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 70 square meters, what are the dimensions of the garden? Use the quadratic formula to find the width.

• Width: 5 meters, Length: 8 meters

• Width: 6 meters, Length: 9 meters

• Width: 8 meters, Length: 11 meters

• Width: 7 meters, Length: 10 meters

A rectangular swimming pool has a length that is twice its width. If the perimeter of the pool is 60 meters, what are the dimensions of the pool? Graph the quadratic function representing the relationship between length and width.

• Length: 30 meters, Width: 15 meters

• Length: 20 meters, Width: 10 meters

• Length: 15 meters, Width: 7.5 meters

• Length: 25 meters, Width: 12.5 meters

A rectangular field has a length that is 5 meters more than twice its width. If the area of the field is 100 square meters, find the dimensions of the field using the quadratic formula.

• Width: 10 meters, Length: 25 meters

• Width: 8 meters, Length: 21 meters

• Width: 7.5 meters, Length: 20 meters

• Width: 5 meters, Length: 15 meters

A square park has a perimeter of 48 meters. If the park is expanded by increasing each side by x meters, express the new area as a quadratic function of x. What is the area when x = 2?

• 64 square meters

• 150 square meters

• 196 square meters

• 100 square meters

A rectangular plot of land has a width of x meters and a length of (x + 4) meters. If the area of the plot is 96 square meters, find the value of x using the quadratic formula.

• 10

• 6

• 8

• 12

A rectangular room has a length that is 4 meters longer than its width. If the area of the room is 32 square meters, find the dimensions of the room and graph the quadratic function that represents this relationship.

• Width: 5 meters, Length: 9 meters

• Width: 3 meters, Length: 7 meters

• Width: 4 meters, Length: 8 meters

• Width: 6 meters, Length: 10 meters

A garden is designed in the shape of a rectangle where the length is 3 meters more than twice the width. If the area of the garden is 45 square meters, find the dimensions using the quadratic formula.

• Width: 3.5 meters, Length: 10 meters

• Width: 5 meters, Length: 13 meters

• Width: 2 meters, Length: 9 meters

• Width: 4 meters, Length: 12 meters

A rectangular fence is to be built around a garden that is 10 meters long and 6 meters wide. If the fence is to be expanded to increase the area by 50 square meters, what will be the new dimensions? Use the quadratic formula to solve.

• 11m by 7m

• 13m by 9m

• 10m by 8m

• 12.5m by 8.5m

A rectangular box has a length that is 3 times its width. If the volume of the box is 81 cubic meters, express the width as a quadratic equation and find its value using the quadratic formula.

• 3√3

• 6√2

• 9

• 3√4

A rectangular plot has a length that is 2 meters longer than its width. If the perimeter is 40 meters, find the dimensions of the plot and graph the quadratic function that represents the relationship between length and width.

• Width: 8 meters, Length: 10 meters

• Width: 10 meters, Length: 12 meters

• Width: 7 meters, Length: 9 meters

• Width: 9 meters, Length: 11 meters