Quadratic by Factoring Worksheets Grade 9

1. A technology company is designing a new smartphone with a rectangular screen. The screen's area is 216 square centimeters, and its length is 6 centimeters more than its width. The engineers need to calculate the exact dimensions to determine the phone's overall size. What are the dimensions of the screen in centimeters?
2. Mason is designing a rectangular fountain on a coordinate grid. One corner of the fountain is at the origin (0,0), and the fountain extends along the positive x-axis and positive y-axis. The length along the x-axis is 8 meters more than the width along the y-axis. The area of the fountain is 84 square meters. Write a quadratic equation in standard form that represents this situation, then solve for the width by factoring.
3. Mere is designing a rectangular patio that will be drawn on a coordinate grid. One corner is at the origin (0,0), and the adjacent sides lie along the positive x-axis and positive y-axis. The length along the x-axis is x meters, and the length along the y-axis is (x + 2) meters. The area of the rectangle is 48 square meters. Write a quadratic equation in standard form that represents this situation, then solve for x by factoring to find the dimensions of the patio.

…and 4 more problems

1. A rectangular parking lot has an area of 180 square meters. The length of the parking lot is 3 meters less than twice its width. What are the dimensions of the parking lot in meters?
2. A rectangular garden has an area of 54 square meters. The length of the garden is 3 meters more than twice its width. Liam needs to build a fence around the entire garden. What are the dimensions of the garden in meters?
3. A right triangle is drawn on a coordinate plane with vertices at (0,0), (x,0), and (0,6). The area of the triangle is 12 square units. Write the quadratic equation in standard form that represents this situation, then solve for x by factoring.

…and 5 more problems

1. Liam is designing a rectangular garden with a path of uniform width around it. The garden itself measures 12 meters by 8 meters. The total area of the garden plus the path is 140 square meters. What is the width of the path in meters?
2. Kaia is designing a rectangular community garden. The area of the garden is 180 square meters. The length of the garden is 3 meters more than its width. What are the dimensions of the garden in meters?
3. A rectangular garden has an area of 54 square meters. The length of the garden is 3 meters more than twice its width. What are the dimensions of the garden?

…and 3 more problems