Square root - practice problems - page 7 of 73

Number of problems found: 1450

Boxes
Petra has planted flowers in two boxes in the shape of a cube. The first box has an internal dimension of 70 cm and the second 5 dm. She wants to make one box in the shape of a cuboid, into which she could transplant both flowers from these boxes. The new
RR trapezoid
Given an isosceles trapezoid ABCD with bases |AB| = 36 m and |CD| = 200 dm, and leg |BC| = 10 m. Calculate the area and perimeter of the trapezoid and the length of diagonal AC.
Table - tablecloth
Mrs. Vránová has a square table with a side length of 110 cm. She wants to have a square tablecloth made for it so that each corner extends 25 cm beyond the edge of the table. What dimensions should the tablecloth have?
Segments on the hypotenuse
A right triangle ABC has a hypotenuse c = 26 cm. The altitude from C to the hypotenuse is h_c = 12 cm. What are the lengths of the two segments of the hypotenuse? What are the lengths of sides a and b? What are the angles at vertices A and B?
Trapezoid 83
Trapezoid ABCD is composed of five triangles. Points E and G divide segment AB in the ratio 2:4:3 (in this order) into three segments. Point F is the midpoint of segment AD. Triangle AEF is isosceles and right-angled. Triangles GBC and CDG are right-angle
In trapezoid 3
In trapezoid ABCD, the following elements are given: lengths of the parallel sides a = 20 cm and c = 11 cm, angle α = 63°36', and angle β = 79°36'. Calculate the lengths of the other two sides and the sizes of the remaining angles.
Given is
The circle is given by the equation x² + y² − 4x + 2y − 11 = 0. Calculate the area of the regular hexagon inscribed in this circle.
Determine 23
Determine in cm² the area of rectangle ABCD, whose longer side is a = 20 cm and whose diagonal is 10 cm longer than its shorter side.
Isosceles gable
The gable of a cottage roof is in the shape of an isosceles triangle with a base of 8 m and legs of 10 m. How high is the gable?
Diagonal 2
What is the area in square metres of a rectangular garden whose diagonal is 50 m long and whose width is 27 m? Round the result to the nearest whole number.
Rhombus - ratio
In a rhombus, the ratio of a side to the height drawn to that side is 4:1, and its area is 49 cm². Calculate the length of the side and the height drawn to that side.
Hypotenuse of ABC
In a right triangle ABC with hypotenuse c, leg a = 6 cm and sin α = 3/5. What is the length of leg b?
Isosceles
A flower bed has the shape of an isosceles triangle with a base of 25 m and legs of 30 m. Calculate the maximum number of flowers that can be planted in this bed, assuming each flower requires approximately 8 dm² of space. Round the result to the nearest
Suitcase - rod
The boot of a car has the shape of a cuboid with dimensions 1.6 m × 1.2 m × 0.5 m (width × depth × height). Determine the longest thin rod that can be placed flat on the bottom of the boot.
Equilateral cone
A cup has the shape of a right circular cone whose slant height equals the diameter of its base (i.e. the axial cross-section is an equilateral triangle). It is supposed to hold 0.2 litres of liquid when filled to 1 cm below the rim. Calculate its diamete
Arbor
Calculate in square metres the area of an arbour whose ground plan is in the shape of a regular hexagon with a side length of 4.5 m.
Chord and radius
Calculate the radius of a circle whose chord XY is 8 cm long and whose centre is 3 cm from the chord.
Rhombus 47
A rhombus has a side length of 5 m and a longer diagonal of 8 m. What is the length of the shorter diagonal?
Regular 4BH
A regular quadrilateral prism has a volume of 864 cm³ and its total surface area is twice the area of its base. Determine the length of its space diagonal.
PT - Pythagorean
A right triangle ABC has hypotenuse c and legs a and b. Estimate the length of the missing side and compare your estimate with the calculated value. a) a = 4 cm; b = 5 cm b) a = 6.8 m; b = 9 m c) a = 8.9 m; b = 1 m d) b = 10 cm; c = 20 cm e) b = 2.5 m; c

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