Quadratic equation + Pythagorean theorem - practice problems - page 2 of 6
Number of problems found: 118
- Side wall planes
Find the volume and surface of a cuboid whose side c is 30 cm long and the body diagonal forms angles of 24°20' and 45°30' with the planes of the side walls. - 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. - 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. - Ratio of squares
A circle is given in which a square is inscribed. The smaller square is inscribed in a circular arc formed by the square's side and the circle's arc. What is the ratio of the areas of the large and small squares?
- 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. - 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]. - 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? - Block or cuboid
The wall diagonals of the block have sizes of √29cm, √34cm, and √13cm. Calculate the surface and volume of the block. - Suppose
Suppose you know that the length of a line segment is 15, x2=6, y2=14, and x1= -3. Find the possible value of y1. Is there more than one possible answer? Why or why not? - 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.
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