Question

The diagonals of a rectangle are 5x + 1 and 9x – 7, respectively. Find the value of x.​

Answer 1

Answer:

⇒ In the 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 a rectangle are equal.

⇒ So, AC = BD

We can also write it as,

⇒ 2×OA=2×OD

⇒ 2×(2x+4) =2×(3x+1)

⇒ 2x+4=3x+1

∴ x=3

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Answer 2

SOLUTION

GIVEN

The diagonals of a rectangle are 5x + 1 and 9x – 7, respectively.

TO DETERMINE

The value of x

EVALUATION

Here it is given that the diagonals of a rectangle are 5x + 1 and 9x – 7, respectively.

We know that diagonals of a rectangle are equal and bisect each other

So by the given condition

5x + 1 = 9x - 7

⇒ 5x - 9x = - 7 - 1

⇒ - 4x = - 8

⇒ x = 2

FINAL ANSWER

Hence the required value of x = 2

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