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.
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.
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.
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.
Calculate the sides of a right triangle if the length of the medians to the legs are ta = 23 cm and tb=14 cm.
- R Trapezium
Rectangular trapezium has bases 17 and 7 and area 80 cm2. What is its perimeter?
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 hc = 19 cm. Determine the length of both trangle legs.
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?
Are diagonals in a rectangular trapezoid perpendicular and bisect the angles?
- Built-up area
John build up area 4.3 x 8 = 34.4 m2 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%?
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.
In right triangle ABC with right angle at C is given side a=29 and height v=27. Calculate the perimeter of the triangle.
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.
Calculate distance between two points Z[7; -9] and U[-10; -8].