Quadratic Challenges: Area & Perimeter Problems for 9th Grade

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?

• Width: 7 meters, Length: 10 meters

• Width: 5 meters, Length: 8 meters

• Width: 6 meters, Length: 9 meters

• Width: 8 meters, Length: 11 meters

A square park has a perimeter of 64 meters. If the park is expanded by increasing each side by 'x' meters, express the new area of the park as a quadratic equation and find the new area when 'x' is 2 meters.

• 324 square meters

• 256 square meters

• 144 square meters

• 400 square meters

The length of a rectangular swimming pool is twice its width. If the perimeter of the pool is 60 meters, find the dimensions of the pool and calculate its area.

• Width: 5 meters, Length: 10 meters, Area: 50 square meters

• Width: 15 meters, Length: 30 meters, Area: 450 square meters

• Width: 10 meters, Length: 20 meters, Area: 200 square meters

• Width: 12 meters, Length: 24 meters, Area: 288 square 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.

• Width: 5 meters, Length: 15 meters

• Width: 4 meters, Length: 14 meters

• Width: 7 meters, Length: 19 meters

• Width: 10 meters, Length: 20 meters

A triangular plot of land has a base that is 4 meters longer than its height. If the area of the triangle is 48 square meters, find the height and base of the triangle.

• Height: 8 meters, Base: 12 meters

• Height: 10 meters, Base: 14 meters

• Height: 6 meters, Base: 10 meters

• Height: 5 meters, Base: 9 meters

A rectangular room has a width that is 2 meters less than its length. If the area of the room is 50 square meters, find the dimensions of the room.

• Length: 6 meters, Width: 4 meters

• Length: 10 meters, Width: 8 meters

• Length: 8 meters, Width: 6 meters

• Length: 7 meters, Width: 5 meters

A rectangular fence is to be built around a garden. If the length is 4 meters more than the width and the total area enclosed is 96 square meters, find the dimensions of the garden.

• Width: 10 meters, Length: 14 meters

• Width: 6 meters, Length: 10 meters

• Width: 5 meters, Length: 9 meters

• Width: 8 meters, Length: 12 meters

A rectangular box has a length that is 3 times its width. If the area of the base of the box is 75 square meters, find the dimensions of the box.

• Width: 10 meters, Length: 30 meters

• Width: 7 meters, Length: 21 meters

• Width: 4 meters, Length: 12 meters

• Width: 5 meters, Length: 15 meters

A rectangular plot of land has a length that is 10 meters longer than its width. If the perimeter of the plot is 80 meters, find the dimensions of the plot and calculate its area.

• Width: 10 meters, Length: 20 meters, Area: 200 square meters

• Width: 15 meters, Length: 25 meters, Area: 375 square meters

• Width: 12 meters, Length: 22 meters, Area: 264 square meters

• Width: 20 meters, Length: 30 meters, Area: 600 square meters

A rectangular painting has a width that is 5 inches less than its length. If the area of the painting is 60 square inches, find the dimensions of the painting.

• Length: 10 inches, Width: 5 inches

• Length: 8 inches, Width: 3 inches

• Length: 15 inches, Width: 10 inches

• Length: 12 inches, Width: 7 inches