# Quadratic equation - high school - math problems

1. Circle and square An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD.
2. Magnified cube If the lengths of the edges of the cube are extended by 5 cm, its volume will increase by 485 cm3. Determine the surface of both the original and the magnified cube.
3. Viewing angle The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure. How far is the observer from the other end of the enclosure?
4. Birthdays In the classroom, students always give candy to their classmates on their birthdays. The birthday person always gives each one candy, and he does not give himself. A total of 650 candies were distributed in the class per year. How many students are in the
5. An equilateral An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?
6. Two groves Two groves A, B are separated by a forest, both are visible from the hunting grove C, which is connected to both by direct roads. What will be the length of the projected road from A to B, if AC = 5004 m, BC = 2600 m and angle ABC = 53° 45 ’?
7. Block or cuboid The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
8. The tourist The tourist wanted to walk the route 16 km at a specific time. He, therefore, came out at the necessary constant speed. After a 4 km walk, however, he fell unplanned into the lake, where he almost drowned. It took him 20 minutes to get to the shore and re
9. Suppose Suppose you know that the length of a line segment is 15, x2=6, y2=14 and x1= -3. Find the possible value of y1. Is there more than one possible answer? Why or why not?
10. TV competition In the competition, 10 contestants answer five questions, one question per round. Anyone who answers correctly will receive as many points as the number of competitors answered incorrectly in that round. One of the contestants after the contest said: We
11. Conical bottle When a conical bottle rests on its flat base, the water in the bottle is 8 cm from it vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle?
12. The product The product of a number plus that number and its inverse is two and one-half. What is the inverse of this number
13. Rectangle field The field has a shape of a rectangle having a length of 119 m and a width of 19 m. , How many meters have to shorten its length and increase its width to maintain its area and circumference increased by 24 m?
14. Three parallels The vertices of an equilateral triangle lie on 3 different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle.
15. A rectangle 2 A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths.
16. Square side If we enlarge the square side a = 5m, its area will increase by 10,25%. How many percent will the side of the square increase? How many percent will it increase the circumference of the square?
17. 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.
18. Before yesterday He merchant adds a sale sign in his shop window to the showed pair of shoes in the morning: "Today by p% cheaper than yesterday. " After a while, however, he decided that the sign saying: "Today 62.5% cheaper than the day before yesterday". Determine the
19. 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.
20. Equation 23 Find value of unknown x in equation: x+3/x+1=5 (problem finding x)

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