# 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 triangle One angle of the triangle is 36° and the remaining two are in the ratio 3:5. Determine whether triangle is a rectangular triangle.
2. Alfa, beta, gama In the triangle ABC is the size of the internal angle BETA 8 degrees larger than the size of the internal angle ALFA and size of the internal angle GAMA is twice the size of the angle BETA. Determine the size of the interior angles of the triangle ABC.
3. Wheel diameter A 1m diameter wheel rolled along a 100m long track. How many times did it turn?
4. Smallest internal angle Calculate what size has the smallest internal angle of the triangle if values of angles α:β:γ = 3:4:8
5. RTriangle 17 The hypotenuse of a right triangle is 17 cm. If you decrease both two legs by 3 cm you will reduce the hypotenuse by 4 cm. Determine the length of this legs. The size of two internal angles of a triangle ABC are α=6/18π and β=7/18π. Calculate the size of the third angle.
7. Right angled From the right triangle with legs 12 cm and 20 cm we built a square with the same content as the triangle. How long will be side of the square?
8. Sides of the triangle Calculate triangle sides where its area is S = 84 cm2 and a = x, b = x + 1, xc = x + 2
9. Pavilion The rectangular pavilion with dimensions 3.5 m and 2.75 m to be paved with square tiles of side 25 cm price of CZK 22 per 1 piece or rectangular tiles with sides of 20 cm and 15 cm in the price of CZK 11 per 1 pc. Which solution is cheaper (write its price
10. Rectangle - sides 3 If in the rectangle ABCD we enlarge the side a by 5 cm and decrease the side b by 2 cm, the rectangle area will be reduced by 5 cm². When we decrease the length of the side a by 4 cm and and at the same time we increase the length of side b by 3 cm we incr
11. Hřiště Map scale is 1: 5000. The playground is rectangular and on the map has dimensions 10 cm and 5 cm What is area of playground in square meters in reality?
12. Engine pulley The engine has a 1460 rev / min (RPM). Disc diameter is 350 mm. What will be the disc peripheral speed in RPM? Pulleys on the engine has diameter 80mm, on a disc has diameter 160mm.
13. Three vectors The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point so that they are in balance. Determine the angles of the each two forces.
14. Perimeter of circle Calculate the circumference of described circle to the triangle with sides 9,12,15 cm.
15. Rhombus A2p Rhombus area is 13 cm2 and its height is 5cm long . Determine a perimeter of this rhombus.
16. Wheel What is the wheel diameter if on the 0.38 km track turns 128 times?
17. Parabola Find the equation of a parabola that contains the points at A[6; -5], B[14; 9], C[23; 6]. (use y = ax2+bx+c)
18. QuizQ An isosceles triangle has two sides of length 7 km and 39 km. How long is a third side?
19. Traffic laws Under traffic regulations, car lights can illuminate the road up to a maximum of 30 m. To check the reach of the dipped-beam lights of their car, Peter stopped car at 1.5 m from the wall. The dipped-beam headlights are 60 cm high. At what height on the wa
20. Clock face clock face is given. Numbers 10 and 5, and 3 and 8 are connected by straight lines. Calculate the size of their angles.

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