Quadratic equation + planimetrics - practice problems - page 10 of 11
Number of problems found: 220
- The hall
The hall had a rectangular ground plan, one dimension 20 m longer than the other. After rebuilding, the length of the hall declined by 5 m, and the width increased by 10 m. The floor area increased by 300 m². What were the original dimensions of the hall? - Circular flowerbed
We split the circular flowerbed with diameter 8 m by concentric circle to circle and annulus with the same area. Find the radius of the circle. - Orchard
The route passes the trapezoidal orchard perpendicular to the parallel sides. It is 80 cm wide. The lengths of the bases are in the ratio 5:3. The length of the longer base to the size of the path is in the ratio of 5:6. How many square meters occupy the - Perimeter and legs
Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg, and its area is 24 cm².
- 3d vector component
The vector u = (3.9, u3), and the length of the vector u is 12. What is, is u3? - Right angled triangle
The hypotenuse of a right triangle is 17 cm long. When we decrease the length of the legs by 3 cm, then decrease its hypotenuse by 4 cm. Find the size of its legs. - Triangle
Calculate the triangle sides if its area S = 630 and the second cathetus is shorter by 17. - Do you solve this?
Determine area S of a rectangle and the length of its sides if its perimeter is 102 cm. - Diagonals in the diamond
The length of one diagonal in a diamond is 24 cm greater than the length of the second diagonal, and the diamond area is 50 m². Determine the sizes of the diagonals.
- Catheti
The hypotenuse of a right triangle is 41, and the sum of legs is 49. Calculate the length of its legs. - Tiles
From how many tiles, 20 cm by 30 cm, we can build a square of maximum dimensions if we have maximum 275 tiles. - Circle
The circle is given by center on S[-7; 10] and maximum chord 13 long. How many intersect points have a circle with the coordinate axes? - Rectangle - sides
A rectangle has an area 266 cm². The length of the shorter side is 5 cm fewer than the length of the longer side. What is the perimeter of a rectangle? - Column
The vertical pole high $v m tall broke, and its toe fell $x m from the bottom of the pole. At what height above the ground does the pole break?
- Rhombus
The rhombus with area 137 has one diagonal that is longer by 5 than the second one. Calculate the length of the diagonals and rhombus sides. - Circle chord
Determine the circle's radius in which the chord 6 cm away from the center is 12 cm longer than the circle's radius. - Built-up area
John build-up area 5 x 7 = 35 m² with building with a wall thickness 30 cm. How many centimeters would he have to subtract from the thickness of the walls that the built-up area fell by 9%? - RT and circles
Solve the right triangle if the radius of the inscribed circle is r=9 and the radius of the circumscribed circle is R=23. - Rhombus and inscribed circle
It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals.
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