Similar triangles

The triangles ABC and XYZ are similar. Find the missing lengths of the sides of the triangles.
a) a = 5 cm b = 8 cm
x = 7.5 cm z = 9 cm

b) a = 9 cm c = 12 cm
y = 10 cm z = 8 cm

c) b = 4 cm c = 8 cm
x = 4.5 cm z = 6 cm

Correct answer:

c1 =  6 cm
y1 =  12 cm
a2 =  6 cm
y2 =  3 cm
a3 =  6 cm
y3 =  3 cm

Step-by-step explanation:

a1=5 cm b1=8 cm x1=7.5 cm z1=9 cm  k1=x1/a1=7.5/5=32=1.5 k1=z1/c1  c1=z1/k1=9/1.5=6 cm
k1=y1/b1 y1=k1 b1=1.5 8=12 cm
b2=4 cm c2=8 cm x2=4.5 cm z2=6 cm  k2=z2/c2=6/8=34=0.75 k2=x2/a2  a2=x2/k2=4.5/0.75=6 cm
k2=y2/b2 y2=k2 b2=0.75 4=3 cm
b3=4 cm c3=8 cm x3=4.5 cm z3=6 cm  k3=z3/c3=6/8=34=0.75 k3=x3/a3  a3=x3/k3=4.5/0.75=6 cm
k3=y3/b3 y3=k3 b3=0.75 4=3 cm



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



avatar




Tips to related online calculators
Check out our ratio 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

Related math problems and questions:

  • Similar triangles
    triangles_2 Triangle A'B'C 'is similar to triangle ABC, whose sides are 5 cm, 8 cm, and 7 cm long. What is the length of the sides of the triangle A'B'C' if its circumference is 80 cm?
  • Similarity coefficient
    triangles In the triangle TMA the length of the sides is t = 5cm, m = 3.5cm, a = 6.2cm. Another similar triangle has side lengths of 6.65 cm, 11.78 cm, 9.5 cm. Determine the similarity coefficient of these triangles and assign similar sides to each other.
  • The triangles
    triangle1 The triangles KLM and ABC are given, which are similar to each other. Calculate the lengths of the remaining sides of the triangle KLM, if the lengths of the sides are a = 7 b = 5.6 c = 4.9 k = 5
  • Similarity of two triangles
    triangles_1 The KLM triangle has a side length of k = 6.3cm, l = 8.1cm, m = 11.1cm. The triangle XYZ has a side length of x = 8.4cm, y = 10.8cm, z = 14.8cm. Are triangle KLM and XYZ similar? (write 0 if not, if yes, find and write the coefficient of a similarity)
  • 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.
  • Similarity
    podobnost ABC is a triangle wherein a = 4 cm, b = 6 cm, c = 8 cm. Is it similar to the triangle DEF: d = 3 cm, e = 4.5 cm, f = 6 cm? If so, determine the ratio of similarity.
  • Similar triangles
    triangles_1 In the triangle DEF is DE = 21cm, EF = 14.7cm, DF = 28cm. The triangle D´E´F´ is similar to the triangle DEF. Calculate the lengths of the sides of the triangle D´E´F´ if the similarity coefficient is one-seventh.
  • Two similar
    triangles_1 Two similar triangles, one has a circumference of 100 cm, the second has sides successively 8 cm, 14 cm, 18 cm longer than the first. Find the lengths of its sides.
  • Sides ratio
    triangle3_1 Calculate the circumference of a triangle with area 84 cm2 if a:b:c = 10:17:21
  • Rectangular triangles
    r_triangles The lengths of corresponding sides of two rectangular triangles are in the ratio 2:5. At what ratio are medians relevant to hypotenuse these right triangles? At what ratio are the contents of these triangles? Smaller rectangular triangle has legs 6 and 8
  • Cutting cone
    kuzel_zrezany A cone with a base radius of 10 cm and a height of 12 cm is given. At what height above the base should we divide it by a section parallel to the base so that the volumes of the two resulting bodies are the same? Express the result in cm.
  • Right triangle - ratio
    rt_triangle The lengths of the legs of the right triangle ABC are in ratio b = 2: 3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle.
  • Center of gravity
    triangles_9 In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT.
  • 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
  • MO - triangles
    metal On the AB and AC sides of the triangle ABC lies successive points E and F, on segment EF lie point D. The EF and BC lines are parallel and is true this ratio FD:DE = AE:EB = 2:1. The area of ABC triangle is 27 hectares and line segments EF, AD, and DB seg
  • 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.
  • Cuboid face diagonals
    face_diagonals_1_1 The lengths of the cuboid edges are in the ratio 1: 2: 3. Will the lengths of its diagonals be the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid.