What is the measurement of a square's side whose diagonal measures ?

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answer is A.

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Detailed Solution

Concept- Assume that the square's side is "a" in length. Use the Pythagorean theorem to solve the ABC triangle, which asserts that the square of the hypotenuse's length equals the sum of the squares of the sides. Consequently, calculate the diagonal AC's length in terms of a. Create an equation in a by equating this expression to

. Solve for a. The square's side length is determined by the value of a.
Question Image

Allow a to be the ABCD square's side length.
The Pythagorean theorem tells us that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of its two other sides.
We obtain the triangle ABC using Pythagoras' theorem.

Putting

, we get

Square root is calculated on both sides to get

But it is given

Hence, we have

The result of dividing both sides by

As a result, the square's side is 16 cm long.
Hence, option 1 is correct.

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