System of equations + triangle - math problems

Number of problems found: 83

One leg
One leg of a right triangle is 1 feet longer than the other leg. The hypotenuse is 5 feet. Find the lengths of the three sides of the triangle.
Two similar
Two similar triangles, one has a circumference of 100 cm, the second has sides successively 8 cm, 14 cm, 18 cm longer than the first. Find the lengths of its sides.
The sides
The sides of a right triangle form an arithmetic sequence. The hypotenuse is 24 cm long. Determine the remaining sides of the triangle.
Outside point
The square ABCD and the point E lying outside the given square are given. What is the area of the square when the distance | AE | = 2, | DE | = 5 a | BE | = 4?
Arm and base
The isosceles triangle has a circumference of 46 cm. Calculate its area if the arm is 5 cm longer than the base.
Railway embankment
The railway embankment section is an isosceles trapezoid, the sizes of the bases of which are in the ratio 5: 3. The arms have a length of 5 m, and the height of the embankment is 4.8 m. Calculates the size of the embankment section area.
There
There is a triangle ABC: A (-2,3), B (4, -1), C (2,5). Determine the general equations of the lines on which they lie: a) AB side, b) height to side c, c) Axis of the AB side, d) median ta to side a
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.
Find the 13
Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3] and C[9, 4].
Coordinates
Determine the coordinates of the vertices and the content of the parallelogram, the two sides of which lie on the lines 8x + 3y + 1 = 0, 2x + y-1 = 0 and the diagonal on the line 3x + 2y + 3 = 0
The tower
The observer sees the tower's base 96 meters high at a depth of 30 degrees and 10 minutes and the top of the tower at a depth of 20 degrees and 50 minutes. How high is the observer above the horizontal plane on which the tower stands?
Side lengths
In the triangle ABC, the height to the side a is 6cm. The height to side b is equal to 9 cm. Side "a" is 4 cm longer than side "b". Calculate the side lengths a, b.
In a
In a triangle, the aspect ratio a: c is 3: 2, and a: b is 5: 4. The perimeter of the triangle is 74cm. Calculate the lengths of the individual sides.
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?
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?
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.
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.
Faces diagonals
If a cuboid's diagonals are x, y, and z (wall diagonals or three faces), then find the cuboid volume. 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.
Touch x-axis
Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.