Planimetry - examples
- Bicycle wheel
After driving 157 m bicycle wheel rotates 100 times. What is the radius of the wheel in cm?
- Diagonals of a rhombus
One of the diagonals of a rhombus is twice as the other. If the sum of the lengths of the diagonals is 24, find the area of the rhombus.
- Right triangle eq2
Hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle.
- Rhombus and diagonals
The a rhombus area is 150 cm2 and the ratio of the diagonals is 3:4. Calculate the length of its height.
- Is right?
Is triangle with sides 24, 51 and 45 right triangle?
From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
- Proof PT
Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
- Reverse Pythagorean theorem
Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 73 m, 66 m, 51 m ? Δ DEF: 63 cm, 105 cm, 84 cm ? Δ GHI: 50 dm, 48 dm, 14 dm ? Δ JKL: 31 m, 45 m, 40 m ? Δ MNO: 28 m, 53 m, 45 m ?
- It is rectangular?
Size of two of the angles in a triangle are: α=60°, β=20°. Is it a right triangle?
Can be rectangular triangle equilateral?
Are two right triangles similar to each other if the first one has a acute angle 10° and second one has acute angle 50°?
- Garden plot
Calculate how many meters of fence need to fence the square garden with length and width of 5 meters.
Is right that in any right triangle height is less or equal half of the hypotenuse?
Prove whether you can construct a triangle ABC, if a=5 cm, b=10 cm, c=2 cm.
Are diagonals in a rectangular trapezoid perpendicular and bisect the angles?
- Triangle P2
Can triangle have two right angles?
In the trapezoid KLMN is given this informations: 1. segments KL and MN are parallel 2. segments KL and KM has same length 3. segments KN, NM and ML has same length. Determine the size of the angle KMN.
- Right Δ
Right triangle has length of one leg 7 cm and length of the hypotenuse 25 cm. Calculate the height of the triangle.
- Center traverse
It is true that the middle traverse bisects the triangle?
May be the largest angle in the triangle less than 70°?