# Quadratic equation - math word problems

#### Number of problems found: 265

- Integer sides

A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side? - Perimeter and diagonal

The perimeter of the rectangle is 82 m, the length of its diagonal is 29 m. Find the dimensions of the rectangle. - On a line

On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1]. - Function 3

Function f(x)=a(x-r)(x-s) the graph of the function has x- intercept at (-4, 0) and (2, 0) and passes through the point (-2,-8). Find constant a, r, s. - 1 page

1 page is torn from the book. The sum of the page numbers of all the remaining pages is 15,000. What numbers did the pages have on the page that was torn from the book? - Lookout tower

How high is the lookout tower? If each step was 3 cm lower, there would be 60 more of them on the lookout tower. If it was 3 cm higher again, it would be 40 less than it is now. - The cylinder

The cylinder has a surface area of 300 square meters, while the height of the cylinder is 12 m. Calculate the volume of this cylinder. - 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 - Dimensions of the trapezoid

One of the bases of the trapezoid is one-fifth larger than its height, the second base is 1 cm larger than its height. Find the dimensions of the trapezoid if its area is 115 cm^{2} - 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 ’? - Roots and coefficient

In the equation 2x ^ 2 + bx-9 = 0 is one root x1 = -3/2. Determine the second root and the coefficient b. - Points in space

There are n points, of which no three lie on one line and no four lies on one plane. How many planes can be guided by these points? How many planes are there if there are five times more than the given points? - 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? - Shell area cy

The cylinder has a shell content of 300 cm square, while the height of the cylinder is 12 cm. Calculate the volume of this cylinder. - 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 - 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? - Derivative problem

The sum of two numbers is 12. Find these numbers if: a) The sum of their third powers is minimal. b) The product of one with the cube of the other is maximal. c) Both are positive and the product of one with the other power of the other is maximal. - Equation 23

Find value of unknown x in equation: x+3/x+1=5 (problem finding x) - Magnified cube

If the lengths of the edges of the cube are extended by 5 cm, its volume will increase by 485 cm^{3}. Determine the surface of both the original and the magnified cube. - 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.

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