Quadratic equation + triangle - practice problems - page 5 of 7
Number of problems found: 125
- Bamboo
At a certain height, the wind broke the bamboo high 32 feet, so the bamboo top reached the ground at a distance of 16 feet from the trunk. At what height from the ground was the bamboo broken? - Right-angled triangle
Determine the area of a right triangle whose side lengths form successive members of an arithmetic progression, and the radius of the circle described by the triangle is 5 cm. - Sphere equation
Obtain the equation of a sphere. Its center is on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1). - Equation of circle 2
Find the equation of a circle that touches the axis of y at a distance of 4 from the origin and cuts off an intercept of length 6 on the axis x.
- Diameter 5668
The span of the arc is 247 cm, and the height of the arc is 21.5 cm. What is the diameter of the circle? - Perpendicular 5516
In a right triangle, one perpendicular is 1 m shorter than the hypotenuse. The other perpendicular is 2 m shorter than the hypotenuse. Find the lengths of all sides of the triangle. - Surface area of the top
A cylinder is three times as high as it is wide. The length of the cylinder diagonal is 20 cm. Find the exact surface area of the top of the cylinder. - Right angled triangle 2
LMN is a right-angled triangle with vertices at L(1,3), M(3,5), and N(6,n). Given angle LMN is 90° find n - Diagonal 20
The rectangular town plaza's diagonal pathway is 20 m longer than the width. Suppose the pathway is 20 m shorter than twice the width. How long should the pathway be?
- Parallelogram 5027
Calculate the area of the parallelogram if the side sizes are a = 80, b = 60, and the size of the diagonal angle is 60°. - Triangle ABC v2
The area of the triangle is 12 cm square. Angle ACB = 30º , AC = (x + 2) cm, BC = x cm. Calculate the value of x. - Right triangle eq2
The hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle. - Circumference 4430
In an isosceles triangle with a circumference of 36 cm, the height at the base is 12 cm long. Calculate the length of the arm of a given triangle. - MO SK/CZ Z9–I–3
John had the ball that rolled into the pool and swam in the water. Its highest point was 2 cm above the surface. The diameter of the circle that marked the water level on the ball's surface was 8 cm. Find the diameter of John's ball.
- Trapezoid
trapezoid ABCD a = 35 m, b=28 m c = 11 m and d = 14 m. How to calculate its area? - Euclid theorems
Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent to the second leg b, is 5cm. - A mast
The wind broke a mast 32 meters high so that its top touches the ground 16 meters from the pole. The still standing part of the mast, the broken part, and the ground form a rectangular triangle. At what height was the mast broken? - Hexagonal prism 2
The regular hexagonal prism has a surface of 140 cm² and a height of 5 cm. Calculate its volume. - RT perimeter
The leg of the rectangular triangle is 7 cm shorter than the second leg and 8 cm shorter than the hypotenuse. Calculate the triangle circumference.
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