# Ratio + triangle - math problems

On solving problems and tasks with proportionally, we recommend hint rule of three. Rule of three (proportionality) help solve examples of direct and inverse proportionality. Three members make possible to calculate the fourth - unknown member.

#### Number of problems found: 113

• Stairway What angle rising stairway if step height in 20 cm and width 26 cm? A meter pole perpendicular to the ground throws a shadow of 40 cm long, the house throws a shadow 6 meters long. What is the height of the house?
• Rectangle 35 Find the area of a rectangle when the diagonal is equal to 30 cms and the width is double the length. The shadow of the tree is 16 meters long. Shadow of two meters high tourist sign beside standing is 3.2 meters long. What height has tree (in meters)?
• Isosceles trapezoid Calculate the area of an isosceles trapezoid whose bases are in the ratio of 4:3; leg b = 13 cm and height = 12 cm.
• Two diagonals The diagonals of the diamond EFGH have lengths in the ratio 1: 2. What is the circumference of a rhombus if the longer of the diagonals is 8 cm long?
• Climb in percentage The height difference between points A and B is 475 m. Calculate the percentage of route climbing if the horizontal distance places A, B is 7.4 km.
• Squares above sides Two squares are constructed on two sides of the ABC triangle. The square area above the BC side is 25 cm2. The height vc to the side AB is 3 cm long. The heel P of height vc divides the AB side in a 2: 1 ratio. The AC side is longer than the BC side. Calc Tree perpendicular to the horizontal surface has a shadow 8.32 meters long. At the same time meter rod perpendicular to the horizontal surface has shadow 64 cm long. How tall is tree?
• Trapezoid ABCD v2 Trapezoid ABCD has length of bases in ratio 3:10. The area of riangle ACD is 825 dm2. What is the area of trapezoid ABCD?
• River Calculate how many permille river Dunaj average falls, if on section long 957 km flowing water from 1454 m AMSL to 101 m AMSL.
• Lookout tower Calculate the height of a lookout tower forming a shadow of 36 m if at the same time a column 2.5 m high has a shadow of 1.5 m.
• Chimney and tree Calculate the height of the factory chimney, which casts a shadow 6.5 m long in the afternoon. At the same time, a 6 m high tree standing near it casts a shadow 25 dm long.
• Vertical rod The vertical one meter long rod casts a shadow 150 cm long. Calculate the height of a column whose shadow is 36 m long at the same time.
• Observer The observer sees a straight fence 100 m long in 30° view angle. From one end of the fence is 102 m. How far is it from another end of the fence?
• The tower The observer sees the base of the tower 96 meters high at a depth of 30 degrees and 10 minutes and the top of the tower at a depth of 20 degrees and 50 minutes. How high is the observer above the horizontal plane on which the tower stands?
• Cone side Calculate the volume and area of the cone whose height is 10 cm and the axial section of the cone has an angle of 30 degrees between height and the cone side.
• Isosceles trapezoid The lengths of the bases of the isosceles trapezoid are in the ratio 5:3, the arms have a length of 5 cm and height = 4.8 cm. Calculate the circumference and area of a trapezoid.
• Diagonal intersect isosceles trapezoid ABCD with length bases | AB | = 6 cm, CD | = 4 cm is divided into 4 triangles by the diagonals intersecting at point S. How much of the area of the trapezoid are ABS and CDS triangles?
• Trapezium diagonals It is given trapezium ABCD with bases | AB | = 12 cm, |CD| = 8 cm. Point S is the intersection of the diagonals for which |AS| is 6 cm long. Calculate the length of the full diagonal AC.

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