Planimetrics - math word problems

Study plane measurements, including angles, distances, and areas. In other words - measurement and calculation of shapes in the plane. Perimeter and area of plane shapes.

1. Let x Let x represent one quantity. State what that quantity represents. Express the second quantity in terms of x. The length of the rectangle is 4 inches less than 8 times the width.
2. Depth angles At the top of the mountain stands a castle, which has a tower 30 meters high. We see the crossroad in the valley from the top of the tower and heel at depth angles of 32° 50 'and 30° 10'. How high is the top of the mountain above the crossroad
3. Area of a rectangle Calculate the area of a rectangle with a diagonal of u = 12.5cm and a width of b = 3.5cm. Use the Pythagorean theorem.
4. Two rectangles 2 A square of area 36 cm2 is cut out to make two rectangles. A and B The area of area A to area B is 2 : 1 Find the dimensions of rectangles A and B.
5. Chauncey Chauncey is building a storage bench for his son’s playroom. The storage bench will fit into the corner and against two walls to form a triangle. Chanuncy wants to buy a triangular shaped cover for the bench. If the storage bench is 2 1/2 ft. Along one w
6. Tree trunk What is the smallest diameter of a tree trunk that we can cut a square-section square with a side length of 20 cm?
7. RPM An electric motor makes 3,000 revolutions per minutes. How many degrees does it rotate in one second?
8. Touch x-axis Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.
9. The second The second angle of a triangle is the same size as the first angle. The third angle is 12 degrees larger than the first angle. How large are the angles?
10. Trapezoid MO The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
11. Garden Area of a square garden is 6/4 of triangle garden with sides 56 m, 35 m, and 35 m. How many meters of fencing need to fence a square garden?
12. Right Δ A right triangle has the length of one leg 7 cm and length of the hypotenuse 25 cm. Calculate the height of the triangle.
13. Hands The clock shows 12 hours. After how many minutes will agle between hour and minute hand 90°? Consider the continuous movement of both hands hours.
14. Circle chord What is the length d of the chord circle of diameter 36 m, if the distance from the center circle is 16 m?
15. Rectangle The rectangle is 21 cm long and 38 cm wide. Determine the radius of the circle circumscribing rectangle.
16. River Calculate how many promiles river Dunaj average falls, if on section long 957 km flowing water from 1454 m AMSL to 101 m AMSL.
17. Trigonometric functions In right triangle is: ? Determine the value of s and c: ? ?
18. Clock How many times a day hands on a clock overlap?
19. Triangle SAS Calculate the area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
20. Movement From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 28 km/h, the second at average speed 24 km/h. Determine the distance between them after 45 minutes cycling.

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