ABCD is a trapezium with ABis parallel CD. The diagonals AC and BD intersect each other at O. If AO = 2x+4, OC=2x-1, DO=3 and OB = 9x-21, Find x.

Open in App

Solution

$ABCD should be a issosceles trapezoid . Diagonal AC = AO + OC = 2 x + 4 + 2 x - 1 = 4 x + 3 BD = DO + OB = 3 + 9 x - 21 = 9 x - 18 As diagonals of trapezium are equal so, 4 x + 3 = 9 x - 18 5 x = 21 x = \frac{21}{5} ANS . . .$

Suggest Corrections

Similar questions

ABCD

is a trapezium such that

B C ∥ A D

and

AD = 4cm .

If the diagonals

AC

and

BD

intersect at O such that

\frac{AO}{OC} = \frac{DO}{OB} = \frac{1}{2}, then BC =

Q. In trapezium

A B C D

, side

A B ∥ C D

and diagonals

A C

and

B D

intersect each other at

O

Prove that:

\frac{O A}{O C} = \frac{O D}{O B}

Q. Diagonals AC and BD of a trapezium ABCD with

A B ∥ D C

intersect each other at the point O ,

\frac{O A}{O C} = ?

Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O. Using a similarity criterion for two triangles, show that

In the adjoining figure, ABCD is 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.

Join BYJU'S Learning Program

ABCD is a trapezium with ABis parallel CD. The diagonals AC and BD intersect each other at O. If AO = 2x+4, OC=2x-1, DO=3 and OB = 9x-21, Find x. ​

ABCD should be a issosceles trapezoid.Diagonal AC=AO+OC=2x+4+2x-1=4x+3BD=DO+OB=3+9x-21=9x-18As diagonals of trapezium are equalso,4x+3=9x-185x=21x=215 ANS...

ABCD is a trapezium with ABis parallel CD. The diagonals AC and BD intersect each other at O. If AO = 2x+4, OC=2x-1, DO=3 and OB = 9x-21, Find x.

$ABCD should be a issosceles trapezoid . Diagonal AC = AO + OC = 2 x + 4 + 2 x - 1 = 4 x + 3 BD = DO + OB = 3 + 9 x - 21 = 9 x - 18 As diagonals of trapezium are equal so, 4 x + 3 = 9 x - 18 5 x = 21 x = \frac{21}{5} ANS . . .$