Question

The figure below is a square. Find the length of side x in simplest radical form with a rational denominator.

Answer 1

`(5√(2) )/(2)`

Explanation:

The square cut in half makes the right side a right triangle.

The equation for these types of questions is short side * square root of 2 = long side

So that means that x *
`√(2)` = 10

So then divide by square root of 2 on both sides to cancel it out

x = 10/
`√(2)`

Then to simplify it multiply the top and bottom by square root of 2, since you can't have an irrational number in the denominator

That makes it
`(10√(2) )/(2)`

Divide 10/2 to make
`(5√(2) )/(2)`

Answer 2

The calculated length of x in the square is 10√2

How to determine the length of x in the square

From the question, we have the following parameters that can be used in our computation:

The square

The square splitted to two gives a 45-45-90 triangle

Given that we have that triangle is a 45-45-90 triangle

Then

Hypotenuse = Leg√2

Where

Hypotenuse = x

Leg = 10

Substitute the known values into the equation

x = 10 * √2

Evaluate

x = 10√2

Hence, the value of x is 10√2