Side lengths

In the triangle ABC, the height to the side a is 6cm. The height to side b is equal to 9 cm. Side "a" is 4 cm longer than side "b". Calculate the side lengths a, b.

Correct answer:

a =  12 cm
b =  8 cm

Step-by-step explanation:

S=a va2=b vb2 a va=b vb   6 a=9 b a=4+b=12 cm  6a9b=0 ab=4  a=12 b=8



We will be pleased if You send us any improvements to this math problem. Thank you!



avatar




Tips to related online calculators
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
See also our trigonometric triangle calculator.

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

Related math problems and questions:

  • Two heights and a side
    triangle_vysky Construct triangle ABC when the given side is c = 7 cm, height to side a va = 5 cm and height to side b: vb = 4 cm.
  • Squares above sides
    pataVysky Two squares are constructed on two sides of the ABC triangle. The square area above the BC side is 25 cm2. The height vc to the side AB is 3 cm long. The heel P of height vc divides the AB side in a 2: 1 ratio. The AC side is longer than the BC side. Calc
  • Construction
    taznice7 Construction the triangle ABC, if you know: the size of the side AC is 6 cm, the size of the angle ACB is 60° and the distance of the center of gravity T from the vertex A is 4 cm. (Sketch, analysis, notation of construction, construction)
  • Rectangular triangle
    rt_triangle_2 The lengths of the rectangular triangle sides with a longer leg of 12 cm form an arithmetic sequence. What is the area of the triangle?
  • Trapezoid
    lichob_2_1 How long are the trapezoid bases with area 24 cm2 and height 3 cm. One base is 3 times longer than the shorter.
  • Katy MO
    reporter_saved6 Kate draw triangle ABC. Middle of AB have mark as X and the center of the side AC as Y. On the side BC wants to find the point Z such that the content area of a 4gon AXZY was greatest. What part of the triangle ABC can maximally occupy 4-gon AXZY?
  • Sides od triangle
    podobnost Sides of the triangle ABC has length 4 cm, 5 cm and 7 cm. Construct triangle A'B'C' that are similar to triangle ABC which has a circumference of 12 cm.
  • Arm and base
    rr_triangle3 The isosceles triangle has a circumference of 46 cm. Calculate its area if the arm is 5 cm longer than the base.
  • The right triangle
    rt_tr540 The right triangle ABC has a leg a = 36 cm and an area S = 540 cm2. Calculate the length of the leg b and the median t2 to side b.
  • 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
  • Right triangle eq2
    rt_2 Hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle.
  • Triangle ABC
    triangles_3 Calculate the sides of triangle ABC with area 1404 cm2 and if a: b: c = 12:7:18
  • Triangle SSA
    trojuhol Construct a triangle ABC if |AB| = 5cm va = 3cm, CAB = 50 °. It is to create the analysis and construction steps.
  • Diamond diagonals
    kosostvorec Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square, and the side length is 13 cm.
  • Draw triangle
    iso_51 Construct an isosceles triangle ABC, if AB = 7cm, the size of the angle ABC is 47°, arms | AC | = | BC |. Measure the size of the BC side in mm.
  • Parallelogram
    kosodlznik3_1 Rhomboid (parallelogram) has a longer side of 50 cm long. The size of its one height is four times the size of its second height. Calculate the length of the shorter side of this rhomboid in the centimeters.
  • Sss triangle
    8_11_12 Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm