# Length + ratio - math problems

#### Number of problems found: 145

• Calculate
Calculate the height of a tree that casts a shadow 22 m long, if you know that at the same time a pillar 2 m high casts a shadow 3 meters long.
• Two places
The actual distance of the two places is 105 km. Find the scale of the map on which this distance is marked by a line 1.2 dm long.
• Aspect ratio
Determine the ratio of the length to the width of a picture frame that is 12 3/4 inches long and 8 1/2 inches wide.
The state Colorado has the shape of a rectangle. The map is sold on 2 posters. The first has dimensions of 70 cm and 50 cm in a scale of 1: 1,000,000. The second poster has dimensions of 175 cm and 125 cm. What is the scale of the second poster?
• A perimeter
A perimeter of a parallelogram is 2.8 meters. The length of one of its sides is equal to one-seventh of the entire perimeter. Find lengths of the sides of the parallelogram.
• Sides of a rectangle
The dimensions of a rectangle are in a 4:12 ratio. If the shorter side length is 12 cm, what is the length of the longer side in centimetres?
• Construct 8
Construct an analytical geometry problem where it is asked to find the vertices of a triangle ABC: the vertices of this triangle must be the points A (1,7) B (-5,1) C (5, -11). the said problem should be used the concepts of: distance from a point to a li
• MIT 1869
You know the length of hypotenuse parts 9 and 16, at which the hypotenuse of a right triangle is divided by a perpendicular running from its opposite vertex. The task is to find the lengths of the sides of the triangle and the length of the line x. This a
• The diamond
The diamond has an area S = 120 cm2, the ratio of the length of its diagonals is e: f = 5: 12. Find the lengths of the side and the height of this diamond.
• A rectangle 4
A rectangle has area 300 and perimeter 80. what is the ratio of the length and width?
• An architect
An architect makes a model of a new house. The model shows a tile patio in the backyard. In the model, each tile has a length of 1/2 inch and a width of 1/6 inch. The actual tiles have a length of 2/3 feet and a width of 2/9 feet. What is the ratio of the
• Cuboid edges
The lengths of the cuboid edges are in the ratio 2: 3: 4. Find their length if you know that the surface of the cuboid is 468 m2.
The three boys moved from start to finish on three different routes A, B, C, always at the same time. Adam drove road A 1500 m long on a scooter. Blake walked route B 600 m long on foot. Cyril got on a scooter on route C after a 90 m walk, then he left th
• Railway embankment
The railway embankment section is an isosceles trapezoid, the sizes of the bases of which are in the ratio 5: 3. The arms have a length of 5 m, and the height of the embankment is 4.8 m. Calculates the size of the embankment section area.
• A cliff
A line from the top of a cliff to the ground passes just over the top of a pole 5 ft high and meets the ground at a point 8 ft from the base of the pole. If the point is 93 ft from the base of the​ cliff, how high is the​ cliff?
• Two villages
Two villages are 11 km and 500 m away. On the map, their distance is determined by a 5 cm long line. Find the scale of the map.
• 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.
• The straight
The straight path rises by 72 cm every 3 m of its length. How many meters will it climb to 350 m?
• The string
They cut 113 cm from the string and divided the rest in a ratio of 5: 6.5: 8: 9.5. The longest part measured 38 cm. Find the original length of the string.
• Gears
The front gear on the bike has 32 teeth and the rear, on the wheel, has 12 teeth. How many times does the bike's rear-wheel turn if you turn the right pedal 30 times? What distance will you go if the circumference of the bicycle wheel is 250 cm?

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