# System of equations + triangle - practice problems

#### Number of problems found: 84

- 11990 perimeter RT

A right triangle has integer side lengths and a perimeter of 11990. In addition, we know that one of its perpendiculars has a prime number length. Find its length. - One leg

One leg of a right triangle is 1 foot 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 its 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.

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