Quadratic equation + planimetrics - practice problems - page 8 of 12
Number of problems found: 222
- Circumference 6040
The picture shows a square net in which the side of one square is 1 cm long. Draw a rectangle with an area of 18 squares with a circumference of 22 cm. - 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. - 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? - Rectangular 5611
The rectangular course is 12 m longer than its width. Suppose its length increases by 10 m and its area increases by 600 square meters. What are its dimensions? - 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. - 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°. - Diamond diagonals
Calculate the diamond's diagonal lengths if its area is 156 cm² and the side length is 13 cm. - Trapezoid 15
The area of a trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1, and height h is x+4 - Rectangle
The rectangle has a perimeter of 75 cm. The diagonal length is 32.5 cm. Determine the length of the sides. - Trapezium
The lengths of parallel sides of a trapezium are (2x+3) and (x+8), and the distance between them is (x+4). If the area of the trapezium is 590, find the value of x.
- 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. - Time gone
The Square of Richard's age equals the age of his mother. When he is two times older, his mom will be 7/2 times older than he. How old are Richard and his mom? - 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. - Rectangle diagonals
It is given a rectangle with an area of 24 cm² and a circumference of 20 cm. The length of one side is 2 cm larger than the length of the second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.
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