Question

PQRS is a rectangle.Diagonals PR and QS meet at a point O.If OP=2x+4,OS=3x+1.Findthe x and QS​

Answer 1

We know that the diagonals of a rectangle bisect each other, then;

2x + 4 = 3x + 1

or, x = 3

Also, QS = 2 × OS

or, QS = 2(3x + 1)

or, QS = 20

HOPE THIS COULD HELP!!!

Answer 2

According the question:-

PQRS is a rectangle,

PR and QS are two diagonals,

two diagonals meet at the point O,

It is known that the diagonals of a rectangle bisect each other,

∴ $2x + 4 = 3x + 1$        ( OP=2x+4, OS=3x+1) given

$3x-2x= 4 -1$

x = 3

here QS = 2 × OS

QS =$2(3x + 1)$

       = 2 ( 3× 3 +1)

       =2 ×10

   $QS = 20$

Ans :- $x =3, and QS= 20$