Question

ABCD is a rectangle with diagonals AC and BD meeting at a point O find x if OA =5x-7 and OD=4x-5 .​

Answer 1

Answer:

Triangle AOB and triangle COD

AO = OC [ GIVEN ]

∠AOB = ∠COD [ VERTICALLY OPPOSITE ANGLES]

BO = OD [ GIVEN ]

So, triangle AOB is congruent to triangle COD [ SAS ]

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Step-by-step explanation:

Answer 2

Given:

ABCD is a rectangle with diagonals AC and BD meet at a point O and

OA =5x-7 and OD=4x-5 .​

To Find:

Value of X.

Solution:

According to the property of the diagonal of the rectangle,

The length of the diagonals is equal. The two diagonals bisect each other.

∴ AC = BD

⇒ 1/2 AC = 1/2BD

⇒ OA = OD

⇒ 5x-7 = 4x-5

⇒ 5x-4x=7-5

⇒ x=2

Hence, the value of x is 2.