# 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.

Result

x =  10 cm

#### Solution:

$a = 12 \ cm \ \\ c = 8 \ cm \ \\ f_{ 1 } = 6 \ cm \ \\ \ \\ f_{ 1 }:a = f_{ 2 }:c \ \\ \ \\ f_{ 2 } = f_{ 1 } \cdot \ \dfrac{ c }{ a } = 6 \cdot \ \dfrac{ 8 }{ 12 } = 4 \ cm \ \\ \ \\ x = f_{ 1 }+f_{ 2 } = 6+4 = 10 = 10 \ \text { cm }$

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!

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

Be the first to comment!

## Next similar math problems:

1. Right angled triangle 2
LMN is a right angled triangle with vertices at L(1,3), M(3,5) and N(6,n). Given angle LMN is 90° find n
2. Slope form
Find the equation of a line given the point X(8, 1) and slope -2.8. Arrange your answer in the form y = ax + b, where a, b are the constants.
3. Triangle
Triangle KLM is given by plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3]. Calculate its area and itsinterior angles.
4. Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
5. Right triangle from axes
A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 square units. The segment passes through the point ( 5,2). What is the slope of the line segment?
6. Find the 5
Find the equation with center at (1,20) which touches the line 8x+5y-19=0
7. Find the 10
Find the value of t if 2tx+5y-6=0 and 5x-4y+8=0 are perpendicular, parallel, what angle does each of the lines make with the x-axis, find the angle between the lines?
8. Cuboids
Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633)
9. Two people
Two straight lines cross at right angles. Two people start simultaneously at the point of intersection. John walking at the rate of 4 kph in one road, Jenelyn walking at the rate of 8 kph on the other road. How long will it take for them to be 20√5 km apar
10. Center
In the triangle ABC is point D[1,-2,6], which is the center of the |BC| and point G[8,1,-3], which is the center of gravity of the triangle. Find the coordinates of the vertex A[x,y,z].
11. Three points 2
The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D.
12. Line
Line p passing through A[-10, 6] and has direction vector v=(3, 2). Is point B[7, 30] on the line p?
13. Points collinear
Show that the point A(-1,3), B(3,2), C(11,0) are col-linear.
14. Line
Straight line passing through points A [-3; 22] and B [33; -2]. Determine the total number of points of the line which both coordinates are positive integers.
15. Slope
Calculate the slope of a line that intersects points (-84,41) and (-76,-32).
16. Perpendicular
What is the slope of the perpendicular bisector of line segment AB if A[9,9] and B[9,-2]?
17. Cone
If the segment of the line y = -3x +4 that lies in quadrant I is rotated about the y-axis, a cone is formed. What is the volume of the cone?