ABCD is a rectangle such that and ,then the area of rectangle ABCD is:

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None of these

answer is B.

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Detailed Solution

Concept: In order to answer this question, we must determine the area of the rectangle using a formula and the definition of the rectangle, which states that its opposite sides must be equal. The Pythagoras theorem is used to calculate the sides of a rectangle, and the formula is provided here.
The formula is:

is the formula for calculating the area of a rectangle.
Additionally, by applying the Pythagorean theorem in a triangle with right angles and the definition of a rectangle has opposite sides being equal,

Making a rectangular diagram and naming it ABCD must come first.
The rectangle's AB, DC, and length are shown in the diagram, and its AD and BC are its sides.
Now, since the opposite sides of a rectangle are equal, we obtain,
Accordingly, AB=CD and AD=BC ————————— 1
Now, in response to the query we've posed,

Triangle ABC has angle B that forms a right triangle, allowing us to use Pythagoras' theorem.

by entering the hypotenuse, perpendicular, and base values in x, y, and z, we obtain

the aforementioned equation in x, y, and z
We get,

By multiplying both sides by x, we obtain.

After squaring both sides of the equation above, we obtain,
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Using this identity, we can now open the formula above and obtain, where

and

When we take equation 3 out of equation 4, we obtain,
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Given that there are only two possible outcome

Considering that y cannot equal 0
So,

In order to find the answer to the given equation, add both sides by 10x.
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Using equation 1 now, we obtain,