# 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? - Laws

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? - Triangle

Can be rectangular triangle equilateral? - Similarity

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. - Height

Is right that in any right triangle height is less or equal half of the hypotenuse? - Triangle

Prove whether you can construct a triangle ABC, if a=5 cm, b=10 cm, c=2 cm. - Trapezoid

Are diagonals in a rectangular trapezoid perpendicular and bisect the angles? - Triangle P2

Can triangle have two right angles? - KLMN

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? - 3-bracket

May be the largest angle in the triangle less than 70°?

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