In the adjoining figure, ABCD is a trapezium in which CD||AB and its diagonals intersect at O If AO=(5x-7)cm, - Maths - Triangles

Question

In the adjoining figure, ABCD is a trapezium in which CD||AB and
its diagonals intersect at O If AO=(5x-7)cm, OC=(2x+1)cm,
DO=(7x-5)cm and OB=(7x+1)cm, find the value of x
Experts, this question is from RS Aggarwal book (Class 10
Mathematics) and the same question's solution is also given on your
website But the values of OB and OD have been interchanged in your
solution so the answer is coming right But is that the correct way
to do this question?? Please give the correct solution Please
answer fast, have to give an assignment tomorrow

Manbar Singh · Accepted Answer

Dear Student,
Q
In the adjoining figure, ABCD is a trapezium, in which BC || AD and
its diagonals intersect at O If AO = (5x-7) cm; OC=(2x+1) cm; DO =
(7x-5) cm and OB=(7x+1) cm, find the value of x

Here is the answer

We know that diagonals of a trapezium divide each other proportionally
So, AOOC = DOOB⇒5x-72x+1 = 7x-57x+1⇒35x2-49x+5x-7 = 14x2+7x-10x-5⇒21x2-41x-2 = 0⇒21x2-42x + x - 2 = 0⇒21xx-2 + 1x-2 = 0⇒21x + 1x-2 = 0⇒x-2 = 0  or  21x+1 = 0⇒x = 2   or  x = -121 rejected