# Right triangle - 7th grade (12y) - examples

1. Horizontal distance The road has a gradient of 8%. How many meters will the road rise on a horizontal distance of 400m?
2. Garden Area of square garden is 6/4 of triangle garden with sides 56 m, 35 m and 35 m. How many meters of fencing need to fence a square garden?
3. Rectangle The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
4. Square Points A[-5,-6] and B[7,-1] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.
5. Is right? Is triangle with sides 51, 56 and 77 right triangle?
6. Cube diagonal Determine length of the cube diagonal with edge 75 mm.
7. Right triangle Alef The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs.
8. Rhombus ABCD Rhombus ABCD, |AC| = 90 cm, |BD| = 49 cm. Calculate the perimeter of the rhombus ABCD.
9. Diagonal Calculate the length of the diagonal of the rectangle ABCD with sides a = 8 cm, b = 7 cm.
10. Reverse Pythagorean theorem Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ? Δ DEF: 55 dm, 82 dm, 61 dm ? Δ GHI: 24 mm, 25 mm, 7 mm ? Δ JKL: 32 dm, 51 dm, 82 dm ? Δ MNO: 51 dm, 45 dm, 24 dm ?
11. It is rectangular? Size of two of the angles in a triangle are: α=110°, β=40°. Is it a right triangle?
12. IS trapezoid Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm.
13. Railways Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters.
14. Right triangle Legs of right are in ratio a:b = 6:8. Hypotenuse has a length of 61 cm. Calculate the perimeter and area of the triangle.
15. 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.
16. Similarity Are two right triangles similar to each other if the first one has a acute angle 70° and second one has acute angle 20°?
17. Kites Boys run kite on a cable of 68 meters long. What is the kite altitude, if the angle from the horizontal plane is 72°?
18. Ladder Ladder 8 m long is leaning against the wall. It foot is 1 m away from the wall. In which height ladder touch the wall?
19. Triangle Can be rectangular triangle equilateral?
20. Octagon We have a square with side 84 cm. We cut the corners to make his octagon. What will be the side of the octagon?

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