The diagonals of a trapezium intersect at point a the ratio of the length of one diagonal from vertex to point a to the entire length of the diagonals is 3:7 then the ratio of its parallel sides is
Answers
Given : The diagonals of a trapezium intersect at point a the ratio of the length of one diagonal from vertex to point a to the entire length of the diagonals is 3:7
To find : ratio of its parallel sides
Solution:
Let say PQRS is a trapezium with PQ ║ RS
Diagonal intersect at a A
=> RA : PR = 3 : 7
=> RA : AP = 3 : 4
Draw a line AB ║ PQ ║ RS intersecting QR at B
AB/ PQ = RA/PR = RB/QR
=> AB/ PQ = 3/7 = RB/QR
=> AB = 3PQ/7
RB/QR = 3/7
1 - RB/QR = 1 - 3/7
=> (QR - RB)/QR = 4/7
=> QB/QR = 4/7
Also
AB/ RS = QA/QS = QB/QR
=> AB/ RS = 4/7
=> AB = 4RS/7
3PQ/7 = 4RS/7
=> 3PQ = 4RS
=> PQ/RS = 4/3
=> PQ : RS = 4 : 3
ratio of its parallel sides is 4 : 3
Learn more:
If the area of a trapezium with parallel sides of length 30 cm and 23 ...
https://brainly.in/question/4717262
In the adjoining figure ABCD is a trapezium into which parallel sides ...
https://brainly.in/question/7825666