find the missing length in this diagram showing a T-square. (reduce the radical to simplist form.

6 cm (one side of triangle)
3 cm ( other side of triangle)
the third side (diagonal line conecting other two sides)= x cm.

Pythagorean theorem?

6^2 + 3^2 = x^2

Solve for x.

To find the missing length (x cm) in the diagram, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the diagonal (hypotenuse) is equal to the sum of the squares of the other two sides.

In this case, we have a right triangle formed by the sides of length 6 cm, 3 cm, and x cm. Applying the Pythagorean theorem, we can write the equation:

6^2 + 3^2 = x^2

Simplifying this equation:

36 + 9 = x^2

45 = x^2

To reduce the radical to its simplest form, we need to find the square root of both sides:

√45 = √x^2

√45 = x

Therefore, the missing length (x) is equal to √45 cm.