Similarity of two triangles

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)

Correct result:

q =  1.3333

Solution:

$$\begin{gathered} k=6.3\text{ cm } \\ l=8.1\text{ cm } \\ m=11.1\text{ cm } \\ x=8.4\text{ cm } \\ y=10.8\text{ cm } \\ z=14.8\text{ cm } \\ k<l<m \\ x<y<z \\ {q}_1=x\mathrm{/}k=8.4\mathrm{/}6.3={\displaystyle \frac{4}{3}}\doteq 1.3333 \\ {q}_2=y\mathrm{/}l=10.8\mathrm{/}8.1={\displaystyle \frac{4}{3}}\doteq 1.3333 \\ {q}_3=z\mathrm{/}m=14.8\mathrm{/}11.1={\displaystyle \frac{4}{3}}\doteq 1.3333 \\ {q}_1=q_2=q_3 \\ q=q_1=1.3333={\displaystyle \frac{4}{3}} \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Center traverse
  It is true that the middle traverse bisects the triangle?
• Hotel rooms
  In the 45 rooms, there were 169 guests, some rooms were three-bedrooms and some five-bedrooms. How many rooms were?
• Theatro
  Theatrical performance was attended by 480 spectators. Women were in the audience 40 more than men and children 60 less than half of adult spectators. How many men, women and children attended a theater performance?
• Equations - simple
  Solve system of linear equations: x-2y=6 3x+2y=4
• Three brothers
  The three brothers have a total of 42 years. Jan is five years younger than Peter and Peter is 2 years younger than Michael. How many years has each of them?
• The dormitory
  The dormitory accommodates 150 pupils in 42 rooms, some of which are triple and some are quadruple. Determine how many rooms are triple and how many quadruples.
• The Chemistry test
  The Chemistry test contained 8 questions, each with 3 points. Peter scored 21 points. How many percent did Peter write a test?
• Days2minutes
  Write a formula that converts x days to y minutes. The formula is:
• Functions f,g
  Find g(1) if g(x) = 3x - x² Find f(5) if f(x) = x + 1/2
• Please help its due tomorrow
  Using one of the following forms x+p=q or px=q write an to represent these problems using x as the unknown variable Emily can jump twice as far as Evan on the broad standing board if Emily can jump 6.5 feet. How many feet can Evan jump?
• Frameworks is bad
  Calculate how many percent will increase the length of an HTML document, if any ASCII character unnecessarily encoded as hexadecimal HTML entity composed of six characters (ampersand, grid #, x, two hex digits and the semicolon). Ie. space as: &#x20;
• Medians 2:1
  Median to side b (tb) in triangle ABC is 12 cm long. a. What is the distance of the center of gravity T from the vertex B? b, Find the distance between T and the side b.
• Construction
  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)
• Tree shadow
  The shadow of the tree is 16 meters long. Shadow of two meters high tourist sign beside standing is 3.2 meters long. What height has tree (in meters)?
• Similarity coefficient
  The triangles ABC and A "B" C "are similar to the similarity coefficient 2. The sizes of the angles of the triangle ABC are α = 35° and β = 48°. Find the magnitudes of all angles of triangle A "B" C ".
• The triangles
  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 coefficient
  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.