Sides of right angled triangle

One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle.

Result

a =  4 m
b =  3 m
c =  5 m

Solution:

a=c1 b=c2  a2+b2=c2   c26c+5=0  p=1;q=6;r=5 D=q24pr=62415=16 D>0  c1,2=q±D2p=6±162 c1,2=6±42 c1,2=3±2 c1=5 c2=1   Factored form of the equation:  (c5)(c1)=0 c>2 c=c1=5  a=c1=51=4=4  m a = c-1 \ \\ b = c-2 \ \\ \ \\ a^2+b^2 = c^2 \ \\ \ \\ \ \\ c^2 -6c +5 = 0 \ \\ \ \\ p = 1; q = -6; r = 5 \ \\ D = q^2 - 4pr = 6^2 - 4\cdot 1 \cdot 5 = 16 \ \\ D>0 \ \\ \ \\ c_{1,2} = \dfrac{ -q \pm \sqrt{ D } }{ 2p } = \dfrac{ 6 \pm \sqrt{ 16 } }{ 2 } \ \\ c_{1,2} = \dfrac{ 6 \pm 4 }{ 2 } \ \\ c_{1,2} = 3 \pm 2 \ \\ c_{1} = 5 \ \\ c_{2} = 1 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (c -5) (c -1) = 0 \ \\ c>2 \ \\ c = c_{ 1 } = 5 \ \\ \ \\ a = c-1 = 5-1 = 4 = 4 \ \text{ m }

Checkout calculation with our calculator of quadratic equations.

b=c2=52=3=3  m b = c-2 = 5-2 = 3 = 3 \ \text{ m }
c=5=5  m c = 5 = 5 \ \text{ m }



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
Looking for help with calculating roots of a quadratic equation?
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.
See also our trigonometric triangle calculator.

Next similar math problems:

  1. Lighthouse
    majak Marcel (point J) lies in the grass and sees the top of the tent (point T) and behind it the top of the lighthouse (P). | TT '| = 1.2m, | PP '| = 36m, | JT '| = 5m. Marcel lies 15 meters away from the sea (M). Calculate the lighthouse distance from the sea
  2. Diagonals at right angle
    image22 In the trapezoid ABCD this is given: AB=12cm CD=4cm And diagonals crossed under a right angle. What is the area of this trapezoid ABCD?
  3. Mast shadow
    horizons Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. Use the law of sines.
  4. Rectangular trapezoid
    right-trapezium-figure The ABCD rectangular trapezoid with the AB and CD bases is divided by the diagonal AC into two equilateral rectangular triangles. The length of the diagonal AC is 62cm. Calculate trapezium area in cm square and calculate how many differs perimeters of the.
  5. Area of iso-trap
    diagons-of-an-isosceles-trapezoid Find the area of an isosceles trapezoid if the lengths of its bases are 16 cm and 30 cm, and the diagonals are perpendicular to each other.
  6. A boy
    angles_6 A boy of height 1.7m is standing 30m away from flag staff on the same level ground . He observes that the angle of deviation of the top of flag staff is 30 degree. Calculate the height of flag staff.
  7. Shadow of tree
    stromcek_3 Miro stands under a tree and watching its shadow and shadow of the tree. Miro is 180 cm tall and its shade is 1.5 m long. The shadow of the tree is three times as long as Miro's shadow. How tall is the tree in meters?
  8. Secret treasure
    max_cylinder_pyramid Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
  9. Two chords
    tetivy Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
  10. Right circular cone
    cut-cone The volume of a right circular cone is 5 liters. Calculate the volume of the two parts into which the cone is divided by a plane parallel to the base, one-third of the way down from the vertex to the base.
  11. Equilateral triangle ABC
    equliateral In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle cont
  12. Shadow
    shadow_1 A meter pole perpendicular to the ground throws a shadow of 40 cm long, the house throws a shadow 6 meters long. What is the height of the house?
  13. Two angles
    rt_1_1 The triangles ABC and A'B'C 'are similar. In the ABC triangle, the two angles are 25° and 65°. Explain why in the triangle A'B'C 'is the sum of two angles of 90 degrees.
  14. Conical bottle
    cone-upside When a conical bottle rests on its flat base, the water in the bottle is 8 cm from it vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle?
  15. MO Z9–I–2 - 2017
    trapezium_3 In the VODY trapezoid, VO is a longer base and the diagonal intersection K divides the VD line in a 3:2 ratio. The area of the KOV triangle is 13.5 cm2. Find the area of the entire trapezoid.
  16. Trapezium diagonals
    stredova sumernost It is given trapezium ABCD with bases | AB | = 12 cm, |CD| = 8 cm. Point S is the intersection of the diagonals for which |AS| is 6 cm long. Calculate the length of the full diagonal AC.
  17. Pyramid cut
    ihlan_rez We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm2. Find the area of the