Free space in the garden

The grandfather's free space in the garden was in the shape of a rectangular triangle with 5 meters and 12 meters in length. He decided to divide it into two parts and the height of the hypotenuse. For the smaller part creates a rock garden, for the larger sows grass. How many square meters has a larger part?

Result

S =  25.562 m2

Solution:

a=5 m b=12 m  c=a2+b2=52+122=13  S1=a b2=5 122=30 m2 S1=c v2  v=2 S1c=2 301360134.6154 m  cc1=a2 cc2=b2  c1=a2c=521325131.9231 m c2=b2c=122131441311.0769 m  S=c2 v2=11.0769 4.61542432016925.562125.562 m2a=5 \ \text{m} \ \\ b=12 \ \text{m} \ \\ \ \\ c=\sqrt{ a^2+b^2 }=\sqrt{ 5^2+12^2 }=13 \ \\ \ \\ S_{1}=\dfrac{ a \cdot \ b }{ 2 }=\dfrac{ 5 \cdot \ 12 }{ 2 }=30 \ \text{m}^2 \ \\ S_{1}=\dfrac{ c \cdot \ v }{ 2 } \ \\ \ \\ v=\dfrac{ 2 \cdot \ S_{1} }{ c }=\dfrac{ 2 \cdot \ 30 }{ 13 } \doteq \dfrac{ 60 }{ 13 } \doteq 4.6154 \ \text{m} \ \\ \ \\ c c_{1}=a^2 \ \\ c c_{2}=b^2 \ \\ \ \\ c_{1}=\dfrac{ a^2 }{ c }=\dfrac{ 5^2 }{ 13 } \doteq \dfrac{ 25 }{ 13 } \doteq 1.9231 \ \text{m} \ \\ c_{2}=\dfrac{ b^2 }{ c }=\dfrac{ 12^2 }{ 13 } \doteq \dfrac{ 144 }{ 13 } \doteq 11.0769 \ \text{m} \ \\ \ \\ S=\dfrac{ c_{2} \cdot \ v }{ 2 }=\dfrac{ 11.0769 \cdot \ 4.6154 }{ 2 } \doteq \dfrac{ 4320 }{ 169 } \doteq 25.5621 \doteq 25.562 \ \text{m}^2



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

Next similar math problems:

  1. Euklid4
    euclid_2 Legs of a right triangle have dimensions 244 m and 246 m. Calculate the length of the hypotenuse and the height of this right triangle.
  2. Equilateral triangle
    rs_triangle_1 The equilateral triangle has a 23 cm long side. Calculate its content area.
  3. Isosceles trapezium
    rr_lichobeznik_2 Calculate the area of an isosceles trapezium ABCD if a = 10cm, b = 5cm, c = 4cm.
  4. Median in right triangle
    rt_triangle In the rectangular triangle ABC has known the length of the legs a = 15cm and b = 36cm. Calculate the length of the median to side c (to hypotenuse).
  5. Euclid2
    euclid In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
  6. Triangle ABC
    lalala In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC.
  7. Triangle IRT
    triangles_5 In isosceles right triangle ABC with right angle at vertex C is coordinates: A (-1, 2); C (-5, -2) Calculate the length of segment AB.
  8. Double ladder
    rr_rebrik The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart?
  9. Right 24
    euclid_theorem Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 unequal segments. The length of one segment is 5 cm. What is the area of the triangle? Thank you.
  10. Euclid 5
    euclid_3 Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
  11. Isosceles IV
    iso_triangle In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.
  12. Isosceles triangle
    triangle2_3 The leg of the isosceles triangle is 5 dm, its height is 20 cm longer than the base. Calculate base length z.
  13. Median
    medians.JPG In triangle ABC is given side a=10 cm and median ta= 13 cm and angle gamma 90°. Calculate length of the median tb.
  14. A truck
    truck_11 A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
  15. Spruce height
    stromcek_7 How tall was spruce that was cut at an altitude of 8m above the ground and the top landed at a distance of 15m from the heel of the tree?
  16. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  17. Holidays - on pool
    pool_4 Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?