# 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. Is right? Determine whether the triangle with legs (catheti) 19.5 cm and 26 cm and length of the hypotenuse 32.5 cm is rectangular?
2. Triangle midpoints Determine coordinates of triangle ABC vertices if we know tirangle sides midpoints SAB [0;3] SBC [1;6] SAC [4;5], its sides AB, BC, AC.
3. Cable Cable consists of 8 strands, each strand consists of 12 wires with diameter d = 0.5 mm. Calculate the cross-section of the cable.
4. Angles by cosine law Calculate the size of the angles of the triangle ABC, if it is given by: a = 3 cm; b = 5 cm; c = 7 cm (use the sine and cosine theorem).
5. Inscribed circle XYZ is right triangle with right angle at the vertex X that has inscribed circle with a radius 5 cm. Determine area of the triangle XYZ if XZ = 14 cm.
6. Minute Two boys started from one place. First went north at velocity 3 m/s and the second to the east with velocity 4 m/s. How far apart they are after minute?
7. Lift The largest angle at which the lift rises is 16°31'. Give climb angle in permille.
8. Rhumbline Find circumference and area of the rhumbline ABCD if the short side AD of which has a length of 5 cm, and the heel of the height from D leading to the AB side divides the AB side into two sections of 3 cm and 4 cm.
9. Rectangle from string String 12m. Make rectangle when one side is two times longer than its width.
10. The chord Calculate a chord length which the distance from the center of the circle (S, 6 cm) equals 3 cm.
11. Ferris wheel Ferris wheel reaches to 22 m tall and moves at the speed of 0.5m/s. During one drive wheel rotates three times. What is the total drive time?
12. Acceleration 2 if a car traveling at a velocity of 80 m/s/south accelerated to a velocity of 100 m/s east in 5 seconds, what is the cars acceleration? using Pythagorean theorem
13. Isosceles right triangle Contents of an isosceles right triangle is 18 dm2. Calculate the length of its base.
14. Chord 2 Point A has distance 13 cm from the center of the circle with radius r = 5 cm. Calculate the length of the chord connecting the points T1 and T2 of contact of tangents led from point A to the circle.
15. Wheel Diameter of motocycle wheel is 52 cm. How many times rotates wheel on roand long 2 km?
16. Tripled square If you tripled the length of the sides of the square ABCD you increases its content by 200 cm2. How long is the side of the square ABCD?
17. Chord 5 It is given circle k / S; 5 cm /. Its chord MN is 3 cm away from the center of the circle . Calculate its length.
18. Right triangle It is given a right triangle angle alpha of 90 degrees beta angle of 55 degrees c = 10 cm use Pythagorean theorem to calculate sides a and b
19. Tiles How many square tiles with the content 121 cm2 has to be ordered for the paving of the square room with a side length of 2.75 meters?
20. Rectangle Perimeter of rectangle is 48 cm. Calculate its dimensions if they are in the ratio 5:3 (width:height)

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