Question

In a rectangle ABCD, the diagonals AC and BD intersect at O. Given AO = 5x + 1 and
DO = 4x + 19, find x.​

Answer 1

Hello there,

(refer my attachment for rough diagram)

as we know,

the diagonals of a rectangle are equal in length.

ie. AC = BD ------- (I)

we are given - AO = 5x + 1 , DO = 4x + 19

Now,

from (i) AC = BD,

we can write AC = 2 × AO

and BD = 2 × DO

ie. -

2 × AO = 2 × DO

2 × (5x+1) = 2 × (4x+19) (putting given values)

10x + 2 = 8x + 38

10x - 8x = 38 - 2

2x = 36

x = 36/2 = 18

therefore, x = 18

HOPE THIS HELPS

THANKS