Quadratic equation + right triangle - practice problems - page 2 of 6
Number of problems found: 110
- A Cartesian framework
1. In a Cartesian framework, the functions f and g we know that: The function (f) is defined by f (x) = 2x², the function (g) is defined by g (x) = x + 3, the point (O) is the origin of the reference, and point (C) is the point of intersection of the grap - Woman's day
We can easily make a heart for mothers for Woman's day by drawing two semicircles on the two upper sides of the square standing on their top. What is the radius of the circle circumscribed by this heart when the length of the side of the square is 1? - Perpendicular 41811
Calculate the area of a right triangle whose longer perpendicular is six dm shorter than the hypotenuse and three dm longer than the shorter perpendicular. - 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.
- 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. - Perimeter and diagonal
The perimeter of the rectangle is 82 m, and the length of its diagonal is 29 m. Find the dimensions of the rectangle. - Integer sides
A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side? - Right-angled 27683
Right-angled triangle XYZ is similar to triangle ABC, which has a right angle at the vertex X. The following applies a = 9 cm, x=4 cm, x =v-4 (v = height of triangle ABC). Calculate the missing side lengths of both triangles. - 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.
- Circle and square
An ABCD square with a side length of 100 mm is given. Calculate the circle’s radius that passes through vertices B, C, and the center of the side AD. - Difference of legs
In a right triangle, the hypotenuse length is 65 m, and the difference between 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? - 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'? - Branches 18533
The right triangle has an area of 225 cm². One of its branches is twice the size of the other. Find the lengths of its hangers.
- Three parallels
The vertices of an equilateral triangle lie on three different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle. - A rectangle 2
A rectangle has a diagonal length of 74cm. Its side lengths are in a ratio of 5:3. Find its side lengths. - 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. - Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base of 4 m and a height of 3 m. Find the container's radius r (and height h) so that they can hide the largest possible treasure. - Medians in right triangle
It is given a right triangle, and 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?
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