Question

the given figure shows a rhombus in which OA = 3x + 7 ,OC = 5x-3 and OD = 10.Find the values of x and y​

Answer 1

Answer:

OA=3x−1

OC=5x−3

OB=2x+1

OD=6x−5

Thediagonalsoftrapeziumdivideeachotherproportionally

OC

OA

=

OD

OB

⇒

(5x−3)

(3x−1)

=

(6x−5)

(2x+1)

⇒(3x−1)(6x−5)=(2x+1)(5x−3)

⇒18x

2

−21x+5=10x

2

−x−3

⇒8x

2

−20x+8=0

⇒2x

2

−5x+2=0

⇒(2x−1)(x−2)=0

⇒x=

2

1

or2

ifweputx=

2

1

inODthevalueofODisnegative

Hence,x=2