Planimetrics + right triangle - practice problems - page 30 of 57
Number of problems found: 1136
- Triangle
Can an equilateral triangle have a right angle? - Numerically 4839
Calculate the diagonal of such a square, for which it holds that its area is equal to its perimeter (without considering units, numerically ...). - Rectangular field
A rectangular field has a diagonal length of 169m. If the length and width are in the ratio of 12:5. Find the dimensions of the field, the perimeter of the field, and the area of the field. - Rhombus and diagonals
The rhombus area is 150 cm2, and the ratio of the diagonals is 3:4. Calculate the length of its height. - Segment
Calculate the segment AB's length if the coordinates of the end vertices are A[10, -4] and B[5, 5]. - Two chords
Calculate the length of chord AB and perpendicular chord BC to the circle if AB is 4 cm from the circle's center and BC 8 cm from the center. - Kite
John a kite, which is diamond-shaped. Its diagonals are 60 cm long and 90 cm long. Calculate: a) the diamond side b) how much paper John needs to make a kite if he needs a paper on both sides and needs 5% of the paper for bending? - Right triangle - ratio
The lengths of the legs of the right triangle ABC are in ratio b = 2:3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle. - Equilateral triangle vs circle
Find the area of an equilateral triangle inscribed in a circle of radius r = 9 cm. What percentage of the circle area does it occupy? - Height
Is it true that the height is less or equal to half of the hypotenuse in any right triangle? - Rectangle 35
Find the rectangle area when the diagonal is equal to 30 cm and the width is double the length. - Rectangle 3-4-5
The sides of the rectangle are in a ratio of 3:4. The length of its diagonal is 20 cm. Calculate the area of the rectangle. - Rectangle
In rectangle ABCD with sides, |AB|=19, |AD|=16 is from point A guided perpendicular to the diagonal BD, which intersects at point P. Determine the ratio (|PB|)/(|DP|). - Area of iso-trap
Find the area of an isosceles trapezoid if the lengths of its bases are 16 cm and 30 cm, and the diagonals are perpendicular to each other. - Right triangle from axes
A line segment has its ends on the coordinate axes and forms a triangle of area equal to 36 square units. The segment passes through the point ( 5,2). What is the slope of the line segment? - Center of gravity and median
In the isosceles triangle ABC, the center of gravity T is 2 cm from the base AB. The median parallel to the AB side measures 4 cm. What is the area of the ABC triangle? - Acute triangle
In the acute triangle KLM, V is the intersection of its heights, and X is the heel of height to the side KL. The axis of the angle XVL is parallel to the side LM, and the angle MKL is 70°. What size are the KLM and KML angles? - Right-angled 66364
From a rectangular board with 2 m and 3 m dimensions, we cut isosceles and right-angled triangles at the corners with an overhang of 40 cm. Calculate the ratio of the rest of the board's areas to its total original area. - Land boundary
The land is a right triangle. Its hypotenuse is 30 meters long, and its circumference is 72 meters. What are the sizes of the remaining sides of the land boundary? - 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.
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