# Planimetry - problems

- Right Δ

Right triangle has length of one leg 7 cm and length of the hypotenuse 25 cm. Calculate the height of the triangle. - Square

Points A[1,5] and B[-4,-5] are adjacent vertices of the square ABCD. Calculate area of the square ABCD. - Slope of track

Calculate the average slope of the rail tracks between Prievidza (309 m AMSL) and Bratislava (152 m AMSL), if the track is 158 km long. - Tangents

To circle with a radius of 98 dm from the point A guided two tangents. The distance of both points of contact is 155 dm. Calculate the distance from point A and circle centre. - Expansion

If one side of the rectangle is larger 3-times and second 4-times, what percentage increases the area of rectangle? - Rectangle - sides ratio

Calculate area of rectangle whose sides are in ratio 1:7 and perimeter is 735. - Medians

Calculate the sides of a right triangle if the length of the medians to the legs are t_{a}= 23 cm and t_{b}=14 cm. - R Trapezium

Rectangular trapezium has bases 17 and 7 and area 80 cm^{2.}What is its perimeter? - Rhombus

Find the length of the other diagonal and area of rhombus. The perimeter of a rhombus is 40 cm and one of the diagonals is of length 10 cm. - Hypotenuse and height

In a right triangle is length of the hypotenuse c = 45 cm and height h_{c}= 19 cm. Determine the length of both trangle legs. - Coins

Arnold had saved up a number of 1-euro coins. He stored coins in a single layer in a square. Left 4 coins. When he make square, which has one more row, missing 35 coins. How many euros he have? - Trapezoid

Are diagonals in a rectangular trapezoid perpendicular and bisect the angles? - Built-up area

John build up area 4.3 x 8 = 34.4 m^{2}with building with a wall thickness 50 cm. How many centimeters would have to subtract from thickness of the walls that built-up area fell by 8%? - 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. - Euclid2

In right triangle ABC with right angle at C is given side a=29 and height v=27. Calculate the perimeter of the triangle. - Euklid4

Legs of a right triangle have dimensions 61 m and 39 m. Calculate the length of the hypotenuse and the height of this right triangle. - EQL triangle

Calculate inradius and circumradius of equilateral triangle with side a=100 cm. - Garden plot

Calculate how many meters of fence need to fence the square garden with length and width of 5 meters. - Descent of road

Road sign informs the gradient is 10.5%. Calculate the angle which average decreases. - Distance

Calculate distance between two points Z[7; -9] and U[-10; -8].

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