# Quadratic equation + expression of a variable from the formula - math problems

- 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. - 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? - A map

A map with a scale of 1: 5,000 shows a rectangular field with an area of 18 ha. The length of the field is three times its width. The area of the field on the map is 72 cm square. What is the actual length and width of the field? - 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? - 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 ’? - Block or cuboid

The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block. - 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? - 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? - Flowerbed

We enlarge the circular flower bed, so its radius increased by 3 m. The substrate consumption per enlarged flower bed was (at the same layer height as before magnification) nine times greater than before. Determine the original flowerbed radius. - A rectangle 2

A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths. - 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? - Radius

Find the radius of the circle with area S = 200 cm². - 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. - 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 - 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. - Equation 23

Find value of unknown x in equation: x+3/x+1=5 (problem finding x) - 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? - 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=1.3, y=1, z=1.2 - 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. - Reciprocal value

How do I calculate a number x that is 9 greater than its reciprocal (1/x)?

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