Identify triangle properties

Since $\angle Q = \angle R$, triangle $PQR$ is isosceles with sides $PQ = PR = 10$ cm. Altitude $PS$ from vertex $P$ to base $QR$ bisects the base in an isosceles triangle.

$PQ = PR = 10 \text{ cm}, SR = \frac{12}{2} = 6 \text{ cm}$

Apply Pythagorean theorem

In the right-angled triangle $PSR$, the hypotenuse is $PR = 10$ cm and the base is $SR = 6$ cm. We find altitude $PS$.

$PS^2 + SR^2 = PR^2$

Calculate length of PS

Substitute the known values into the equation: $PS^2 + 6^2 = 10^2$, so $PS^2 = 100 - 36 = 64$. Taking the square root gives $PS = 8$ cm.

$PS = \sqrt{64} = 8 \text{ cm}$