# Quadratic equation + right triangle - math problems

#### Number of problems found: 69

- 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. - Two chords

From the point on the circle with a diameter of 8 cm, two identical chords are led, which form an angle of 60°. Calculate the length of these chords. - 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 ’? - 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. - Isosceles triangle

In an isosceles triangle ABC with base AB; A [3,4]; B [1,6] and the vertex C lies on the line 5x - 6y - 16 = 0. Calculate the coordinates of vertex C. - Difference of legs

In a right triangle, the length of the hypotenuse is 65 m, and the difference of legs is 23 m. Calculate the perimeter of this triangle. - 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? - 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. - 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. - 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 - 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. - Perimeter of RT

Find the circumference of the rectangular triangle if the sum of its legs is 22.5 cm and its area is 62.5 cm^{2}. - Rectangle

There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of rectangle. - A rectangle 2

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

Find radius of circle using pythagorean theorem where a=9, b=r, c= 6+r - Touch x-axis

Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis. - 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? - RT sides

Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.

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