Radical Equations Worksheets Grade 9

1. A right triangle is positioned on a coordinate plane with vertices at (0,0), (12,0), and (0,5). A circle is drawn such that it is tangent to the hypotenuse and to both legs of the triangle. What is the radius of this inscribed circle?
2. √(2x + 5) - 3 = 0
3. A right triangle is drawn on a coordinate plane with vertices at (0,0), (15,0), and (0,8). A circle is inscribed inside this triangle such that it touches all three sides. What is the radius of this inscribed circle?

…and 5 more problems

1. Olivia is examining a square drawn on a coordinate plane with vertices at (0,0), (s,0), (s,s), and (0,s). A circle is inscribed inside this square. The area of the circle is given by the expression 49π square units. What is the value of s?
2. Sophia is a safety inspector testing the braking distance of a new electric vehicle. The braking distance d (in meters) on a dry road is given by the formula d = √(0.5v + 13), where v is the speed of the car in kilometers per hour (km/h) just before braking. During a test, the vehicle's braking distance is measured as exactly 7 meters. What was the speed of the car just before braking, in km/h?
3. √(5x + 25) - 10 = 0

…and 4 more problems

1. √(5x - 11) + 2 = 9
2. Liam is designing a rectangular garden with an area of 54 square meters. The length of the garden is 3 meters more than twice its width. Write and solve an equation to determine the width of Liam's garden.
3. Tane is a robotics engineer designing a drone. The drone's altitude (in meters) above the ground during a test flight is modeled by the function h(t) = sqrt(4t + 144), where t is the time in seconds after launch. For a safety check, the drone must reach an altitude of exactly 16 meters. How many seconds after launch will the drone be at this altitude?

…and 5 more problems