Question

ABCD is a rectangle. Its diagonals meet at O. OA = 2x – 1, OD = 3x – 2. Find x

Answer 1

Answer:

value of x is 3

Step-by-step explanation:

In given figure ABCD is a rectangle.

OA=2x+4 and OD=3x+1 [Given]

AC and BD are diagonals of a rectangle.

We know that diagonals of rectangle are equal.

So, AC = BD

We can also write it as,

2×OA=2×OD

⇒2(2x+4)= 2(3x+1)

divide both side by 2

⇒ 2x+4=3x+1

⇒ 2x-3x=1-4

⇒ -x=-3

∴ x=3

Answer 2

Solution :-

given that,

• ABCD is a rectangle.
• Its diagonals meet at O.
• OA = 2x – 1 .
• OD = 3x – 2 .

Since we know that,

• Diagonals of a rectangle are equal and bisect each other .
• So, OA = OC = OB = OD .

then,

→ OA = OD

→ 2x - 1 = 3x - 2

→ 3x - 2x = -1 + 2

→ x = 1 (Ans.)

Hence, value of x is equal to 1 .

Proof :-

→ AC = BD { Diagonal are equal }

So,

→ (1/2)AC = (1/2)BD

also, Point O bisect both diagonals .

→ AO = OD .

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