Land boundary

The land has the shape of a right triangle. The hypotenuse has a length of 30m. The circumference of the land is 72 meters. What is the length of the remaining sides of the land boundary?

Correct result:

a =  24 m
b =  18 m


c=30 m o=72 m  c2=a2+b2 o=a+b+c c2=a2+(oac)2  302=a2+(42a)2  302=a2+(42a)2  2a2+84a864=0 2a284a+864=0  p=2;q=84;r=864 D=q24pr=84242864=144 D>0  a1,2=q±D2p=84±1444 a1,2=84±124 a1,2=21±3 a1=24 a2=18   Factored form of the equation:  2(a24)(a18)=0  a=a1=24 mc=30 \ \text{m} \ \\ o=72 \ \text{m} \ \\ \ \\ c^2=a^2+b^2 \ \\ o=a+b+c \ \\ c^2=a^2 + (o-a-c)^2 \ \\ \ \\ 30^2=a^2 + (42-a)^2 \ \\ \ \\ 30^2=a^2 + (42-a)^2 \ \\ \ \\ -2a^2 +84a -864=0 \ \\ 2a^2 -84a +864=0 \ \\ \ \\ p=2; q=-84; r=864 \ \\ D=q^2 - 4pr=84^2 - 4\cdot 2 \cdot 864=144 \ \\ D>0 \ \\ \ \\ a_{1,2}=\dfrac{ -q \pm \sqrt{ D } }{ 2p }=\dfrac{ 84 \pm \sqrt{ 144 } }{ 4 } \ \\ a_{1,2}=\dfrac{ 84 \pm 12 }{ 4 } \ \\ a_{1,2}=21 \pm 3 \ \\ a_{1}=24 \ \\ a_{2}=18 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 2 (a -24) (a -18)=0 \ \\ \ \\ a=a_{1}=24 \ \text{m}

Checkout calculation with our calculator of quadratic equations.

b=a2  b=oac=722430=18 mb=a_{2} \ \\ \ \\ b=o-a-c=72-24-30=18 \ \text{m}

Try calculation via our triangle calculator.

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!

Tips to related online calculators
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
Pythagorean theorem is the base for the right triangle calculator.
Do you want to convert length units?
See also our trigonometric triangle calculator.

We encourage you to watch this tutorial video on this math problem: video1   video2

Next similar math problems:

  • 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?
  • Catheti
    pyt_theorem The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs.
  • 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.
  • Triangle - is RT?
    triangle_3_angles Triangle has a circumference of 90 cm. Side b is 1 cm longer than c, side c is 31 cm longer than side a. Calculate the length of sides and determine whether triangle is a right triangle.
  • Length IT
    lich2 Find the length (circumference) of an isosceles trapezoid in which the length of the bases a,c and the height h are given: a = 8 cm c = 2 cm h = 4 cm
  • Euclid 5
    euclid_3 Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
  • 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.
  • Sailing
    ship_2 Solve the following problem graphically. The fishing boat left the harbor early in the morning and set out to the north. After 12 km of sailing, she changed course and continued 9 km west. Then she docked and launched the nets. How far was she from the pl
  • Medians and sides
    3angle Determine the size of a triangle KLM and the size of the medians in the triangle. K=(-5; -6), L=(7; -2), M=(5; 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.
  • Is right triangle
    triangle_1111_4 Decide if the triangle XYZ is rectangular: x = 4 m, y = 6 m, z = 4 m
  • Right triangles
    PT How many right triangles we can construct from line segments 3,4,5,6,8,10,12,13,15,17 cm long? (Do not forget to the triangle inequality).
  • 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?
  • ABS CN
    complex_num Calculate the absolute value of complex number -15-29i.
  • RT triangle and height
    345 Calculate the remaining sides of the right triangle if we know side b = 4 cm long and height to side c h = 2.4 cm.
  • 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.
  • Cans
    konzervy How many cans must be put in the bottom row if we want 182 cans arrange in 13 rows above so that each subsequent row has always been one tin less? How many cans will be in the top row?