Question

The figure shows a square with sides of length 1 and a diameter of length x.

How can you determine the value of x?

Find x.
Pls help i don’t know what this is or how to figure it out

Answer 1

• √2 units

Explanation:

It should be diagonal not diameter.

The diagonal of the square is √2 time the side.

The side given 1 unit, then the diagonal is x = √2 units

Answer 2

9514 1404 393

Answer:

x = √2

Explanation:

Perhaps you've heard of the Pythagorean theorem. It tells you the relationship between the sides (a, b) of a right triangle and the hypotenuse (c) is ...

c² = a² + b²

The diagonal of the square (diameter) is the hypotenuse of a right triangle with legs that are the sides of the square. Using the above relation, we have ...

x² = 1² + 1²

x² = 2

x = √2 . . . . . . the length of the diagonal (diameter)

_____

Additional comment

The "take-away" from this is that an isosceles right triangle (one of the two "special" triangles) has side ratios of ...

side : side : hypotenuse = 1 : 1 : √2

(You will see this again.)