Question

BEND is a rectangle. Find x if OB=4x+2 and OD=3x+5. Diagonals meet at point O.

Answer 1

angles of a rectangle are divided in equal parts by each other
so,OB=OD
4x+2=3x+5
4x-3x=5-2
x=3

Answer 2

hey mate here is your answer :-) :-)
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solution :- BO and OD is the half diagonals of BD.
ON and OE is the half diagonals of EN.
As, we know that the diagonals of a rectangle are equal. so, their halves are also equal.

BO = OD
OE = ON
BO = ON
BO = OE
OD = OE
OD = ON

A. T. Q ( according to question ) :-
BO = OD
4x + 2 = 3x + 5
4x - 3x = 5 - 2
x = 3

therefore x = 3

BO = 4x + 2
= 4 (3) +2
= 12 + 2
= 14

OD = 3x + 5
= 3 (3) + 5
= 9 + 5
= 14

hence, proved BO = OD
so, all the diagonals and the halves of their diagonals of a rectangle are equal.

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