# Triangle + perimeter - math problems

1. Triangle from median Calculate the perimeter, content, and magnitudes of the remaining angles of triangle ABC, given: a = 8.4; β = 105° 35 '; and median ta = 12.5.
2. In a In a triangle, the aspect ratio a: c is 3: 2 and a: b 5: 4. The perimeter of the triangle is 74cm. Calculate the lengths of the individual sides.
3. The bases The bases of the isosceles trapezoid ABCD have lengths of 10 cm and 6 cm. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and content of the ABCD trapezoid.
4. Medians in RT The rectangular triangle ABC has a length of 10 cm and 24 cm. Points P, Q, R are the centers of the sides of this triangle. The perimeter of the PQR triangle is:
5. Triangular prism - regular The regular triangular prism is 7 cm high. Its base is an equilateral triangle whose height is 3 cm. Calculate the surface and volume of this prism.
6. Horses playground The fence for the horses has the shape of a rectangular trapezoid with an area of 400 m2, the base lengths should be 31 m and 19 m. How many meters of boards will they need to fence it if the boards are stacked in 5 rows?
7. Triangular prism The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism.
8. Perimeters A rectangle has a perimeter of 16p centimeters, it had a width of 2p centimeters. Each side of an equilateral triangle is 1/2 the length of the rectangle. Find the total perimeter of the rectangle and the triangle if p=8.
9. Land boundary The land has the shape of a right triangle. The hypotenuse has a length of 30m. The circumference of the land is 72 meters. What is the length of the remaining sides of the land boundary?
10. Circular railway The railway is to interconnect in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, BC | = 70 km. How long will the track from A to C?
11. An equilateral triangle The perimeter of an equilateral triangle is 33cm. How long is each side?
12. 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.
13. Ratio of sides Calculate the area of a circle that has the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
14. Perimeter of RT Find the circumference of the rectangular triangle if the sum of its legs is 22.5 cm and its area is 62.5 cm2.
15. Diamond and diagonals A diamond has diagonals f = 8 cm and g = 6 cm long. How long is this diamond perimeter? (Calculate it!)
16. Triangular prism Calculate a triangular prism if it has a rectangular triangle base with a = 4cm and hypotenuse c = 50mm and height of the prism is 0.12 dm.
17. The sides 2 The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.
18. Isosceles triangle In an isosceles triangle, the length of the arm and the length of the base are in ration 3 to 5. What is the length of the arm?
19. Triangle perimeter Calculate the triangle perimeter whose sides are in ratio 3: 5: 7 and the longest side is 17.5 cm long.
20. Circle described The radius of the circle described to the right triangle with 6 cm long leg is 5 cm. Calculate the circumference of this triangle.

Do you have an interesting mathematical word problem that you can't solve it? Submit math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...