Quadratics in Area and Perimeter: Grade 9 Challenges

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: 6 meters, Length: 9 meters

• Width: 8 meters, Length: 11 meters

• Width: 5 meters, Length: 8 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 value of 'x' if the new area is 144 square meters.

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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: 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

• Width: 5 meters, Length: 10 meters, Area: 50 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: 8 meters, Length: 21 meters

• Width: 10 meters, Length: 25 meters

• Width: 12 meters, Length: 29 meters

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

• Height: 10 meters, Base: 14 meters

• Height: 6 meters, Base: 10 meters

• Height: 4 meters, Base: 8 meters

• Height: 8 meters, Base: 12 meters

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

• Width: 5 meters, Length: 15 meters

• Width: 5 meters, Length: 13 meters

• Width: 4 meters, Length: 10 meters

• Width: 6 meters, Length: 12 meters

A rectangular plot of land has a width of 'w' meters and a length of 'w + 10' meters. If the area of the plot is 200 square meters, find the value of 'w' and the dimensions of the plot.

• Width: 12 meters, Length: 22 meters

• Width: 15 meters, Length: 25 meters

• Width: 10 meters, Length: 20 meters

• Width: 5 meters, Length: 15 meters

A square-shaped flower bed has an area of 81 square meters. If the bed is surrounded by a path that is 'x' meters wide, express the area of the flower bed plus the path as a quadratic equation and find 'x' if the total area is 145 square meters.

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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 extended by 'x' meters on each side, write a quadratic equation for the new area of the garden and find 'x' if the new area is 144 square meters.

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A rectangular box has a length that is 4 cm longer than its width. If the volume of the box is 96 cubic centimeters and the height is 3 cm, find the dimensions of the box.

• Width: 5 cm, Length: 9 cm, Height: 3 cm

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

• Width: 4 cm, Length: 8 cm, Height: 3 cm

• Width: 6 cm, Length: 10 cm, Height: 3 cm