# 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°?
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?

Do you have an interesting mathematical example that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.