Trapezium diagonals

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.

Correct result:

x =  10 cm

Solution:

a=12 cm c=8 cm f1=6 cm  f1:a=f2:c  f2=f1 ca=6 812=4 cm  x=f1+f2=6+4=10 cma=12 \ \text{cm} \ \\ c=8 \ \text{cm} \ \\ f_{1}=6 \ \text{cm} \ \\ \ \\ f_{1}:a=f_{2}:c \ \\ \ \\ f_{2}=f_{1} \cdot \ \dfrac{ c }{ a }=6 \cdot \ \dfrac{ 8 }{ 12 }=4 \ \text{cm} \ \\ \ \\ x=f_{1}+f_{2}=6+4=10 \ \text{cm}



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!





Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:
avatar




Tips to related online calculators
Check out our ratio calculator.
See also our trigonometric triangle calculator.

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

Next similar math problems:

  • KLMN
    trapezium In the trapezoid KLMN is given this informations: 1. segments KL and MN are parallel 2. segments KL and KM has same length 3. segments KN, NM and ML has same length. Determine the size of the angle KMN.
  • Isosceles trapezoid
    lichobeznik_6 In an isosceles trapezoid KLMN intersection of the diagonals is marked by the letter S. Calculate the area of trapezoid if /KS/: /SM/ = 2:1 and a triangle KSN is 14 cm2.
  • Isosceles trapezoid v3
    rovnobezky_uhly In an isosceles trapezoid ABCD is the size of the angle β = 81° Determine size of angles α, γ and δ.
  • Median
    tazisko The median of the triangle LMN is away from vertex N 84 cm. Calculate the length of the median, which start at N.
  • Slope
    slope_1 Find the slope of the line: x=t and y=1+t.
  • Similarity coefficient
    trig12 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 ".
  • Angles
    triangle_1111_1 In the triangle ABC, the ratio of angles is: a:b = 4: 5. The angle c is 36°. How big are the angles a, b?
  • Center traverse
    trianles It is true that the middle traverse bisects the triangle?
  • Tree shadow
    tree3 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)?
  • Type of triangle
    237_triangle How do I find the triangle type if the angle ratio is 2:3:7 ?
  • Chord of triangle
    triangle_1212 If the whole chord of the triangle is 14.4 cm long, how do you calculate the shorter and longer part?
  • Supplementary angles
    acuteangles One of the supplementary angles are three times larger than the other. What size is larger of supplementary angles?
  • The angles
    trojuholnik The angles in the triangle are in the ratio 12: 15: 9. Find the angles.
  • Find the 9
    obtuse_triangle_1 Find the missing angle in the triangle and then name triangle. Angles are: 95, 2x+15, x+3
  • 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?
  • Book read
    books_12 If Petra read 10 pages per day, she would read the book two days earlier than she read 6 pages a day. How many pages does a book have?
  • 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.