# Quadratic equation + triangle - math problems

1. Sides of right angled triangle One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle.
2. Secret treasure Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
3. Medians in right triangle It is given a right triangle, angle C is 90 degrees. I know it medians t1 = 8 cm and median t2 = 12 cm. .. How to calculate the length of the sides?
4. Faces diagonals If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.2, y=1.7, z=1.45
5. Two chords Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
6. Trapezoid MO The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
7. Right triangle Alef The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs.
8. MO SK/CZ Z9–I–3 John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
9. Right triangle Legs of the right triangle are in the ratio a:b = 2:8. The hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle.
10. R triangle Calculate the area of a right triangle whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg.
11. Euclid1 Right triangle has hypotenuse c = 27 cm. How large sections cuts height hc=3 cm on the hypotenuse c?
12. Hypotenuse and height In a right triangle is length of the hypotenuse c = 56 cm and height hc = 4 cm. Determine the length of both trangle legs.
13. RT - hypotenuse and altitude Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments?
14. Trapezoid trapezoid ABCD a = 35 m, b=28 m c = 11 m and d = 14 m. How to calculate its area?
15. Euclid theorems Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent the second leg b is 5cm.
16. Diagonal 20 Diagonal pathway for the rectangular town plaza whose length is 20 m longer than the width. if the pathway is 20 m shorter than twice the width. How long should the pathway be?
17. 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
18. Triangle ABC Triangle ABC has side lengths m-1, m-2, m-3. What has to be m to be triangle a) rectangular b) acute-angled?
19. Two triangles SSA Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. A = 59°, a = 13, b = 14
20. Triangle ABC v2 Area of the triangle is 12 cm square. Angle ACB = 30º , AC = (x + 2) cm, BC = x cm. Calculate the value of x.

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