# Quadratic equation + system of equations - math problems

#### Number of problems found: 79

- 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? - Speed of car

The car went to a city that was 240 km away. If his speed increased by 8 km/h, it would reach the finish one hour earlier. Determine its original speed. - Consecutive members

The block has a volume of 1728 cm³. Determine the lengths of the edges a, b, c of the blocks for which a < b < c and a + b + c = 38 cm and whose numerical values in cm represent three consecutive members of the geometric sequence. - Block or cuboid

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

The surfaces of two cubes, one of which has an edge of 22 cm longer than the second are differ by 19272 cm^{2}. Calculate the edge length of both cubes. - Two trucks

Two trucks left cities A and B against each other and met after an hour. The first car came to B 27 minutes later than the second car to A. Calculate the car speed if the distance between cities A, B is 90 km. - Euler problem

Someone buys a 180 tolars towels. If it was for the same money of 3 more towels, it would be 3 tolars cheaper each. How many were towels? - Trapezoid

trapezoid ABCD a = 35 m, b=28 m c = 11 m and d = 14 m. How to calculate its area? - The cylinder

In a rotating cylinder it is given: the surface of the shell (without bases) S = 96 cm^{2}and the volume V = 192 cm cubic. Calculate the radius and height of this cylinder. - Water reservoir

The water reservoir is filled through one inlet 4 hours later than both together, then another inlet 9 hours later than both together. For how long is filled by each separately? - Sphere from tree points

Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a - 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? - Right triangle Alef

The obvod of a right triangle is 84 cm, and the hypotenuse is 37 cm long. Determine the lengths of the legs. - 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. - Digit sum

The digit sum of the two-digit number is nine. When we turn figures and multiply by the original two-digit number, we get the number 2430. What is the original two-digit number? - RTriangle 17

The hypotenuse of a right triangle is 17 cm. If you decrease both two legs by 3 cm you will reduce the hypotenuse by 4 cm. Determine the length of this legs. - 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. - Right angled triangle

Hypotenuse of a right triangle is 17 cm long. When we decrease length of legs by 3 cm then decrease its hypotenuse by 4 cm. Determine the size of legs. - The gardener

The gardener bought trees for 960 CZK. If every tree were cheaper by 12 CZK, he would have gotten four more trees for the same money. How many trees did he buy? - Rectangle vs square

One side of the rectangle is 1 cm shorter than the side of the square, the second side is 3 cm longer than the side of the square. Square and rectangle have the same content. Calculate the length of the sides of a square and a rectangle.

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