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)

Result

q =  1.333

Solution:

$k=6.3 \ \text{cm} \ \\ l=8.1 \ \text{cm} \ \\ m=11.1 \ \text{cm} \ \\ \ \\ x=8.4 \ \text{cm} \ \\ y=10.8 \ \text{cm} \ \\ z=14.8 \ \text{cm} \ \\ \ \\ k<l<m \ \\ x<y<z \ \\ q_{1}=x/k=8.4/6.3 \doteq \dfrac{ 4 }{ 3 } \doteq 1.3333 \ \\ q_{2}=y/l=10.8/8.1 \doteq \dfrac{ 4 }{ 3 } \doteq 1.3333 \ \\ q_{3}=z/m=14.8/11.1 \doteq \dfrac{ 4 }{ 3 } \doteq 1.3333 \ \\ \ \\ q_{1}=q_{2}=q_{3} \ \\ \ \\ q=q_{1}=1.3333 \doteq \dfrac{ 4 }{ 3 } \doteq 1.3333 \doteq 1.333$

Try another example

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:

Be the first to comment!

Next similar math problems:

1. 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
2. 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 ".
3. 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)?
4. 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.
5. Possible lengths
   Find the most possible lengths for the third side of a triangle with sides 20 and 18.
6. Center traverse
   It is true that the middle traverse bisects the triangle?
7. 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?
8. 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;
9. Days2minutes
   Write a formula that converts x days to y minutes. The formula is:
10. Functions f,g
    Find g(1) if g(x) = 3x - x² Find f(5) if f(x) = x + 1/2
11. Reward
    Janko and Peter divided the reward from the brigade so that Peter got 5/8 of the reward. What percentage of Janko's reward got?
12. Mushrooms
    Eva and Jane collected 114 mushrooms together. Eve found twice as much as Jane. How many mushrooms found each of them?
13. Equations
    Solve following system of equations: 6(x+7)+4(y-5)=12 2(x+y)-3(-2x+4y)=-44
14. Art school
    Every fifth pupil 9A goes to art school. How many percent of pupils in class 9A go to art school?
15. 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?
16. Equations - simple
    Solve system of linear equations: x-2y=6 3x+2y=4
17. The ball
    The ball was discounted by 10 percent and then again by 30 percent. How many percent of the original price is now?