PQR is a right angled triangle inwhich \( m \angle \mathrm{Q}=90^{\circ} \), \( m \overline{\mathrm{PR}}=20 \mathrm{~cm}, m \overline{\mathrm{PQ}}=16 \mathrm{~cm} \) and \( m \overline{\mathrm{QR}}=12 \mathrm{~cm} \)

In the world of geometry, right-angled triangles have been fascinating to mathematicians for centuries. The famous Pythagorean theorem, discovered in ancient Greece, tells us that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. So, in triangle PQR, with \( m \overline{\mathrm{PR}} = 20 \mathrm{~cm} \) as the hypotenuse, we can verify its dimensions with this theorem: \( 20^2 = 16^2 + 12^2 \), or \( 400 = 256 + 144 \). Yep, it checks out! Now, let's see where you can apply this knowledge practically! Right-angled triangles are everywhere in real life, from architecture to navigation. If you're trying to figure out the height of a tree or a building, you can measure the distance from the building and your angle of elevation—you'll often form a right triangle. You could also use the Pythagorean theorem when building ramps, creating stable structures, or even in art when planning out the dimensions of triangular shapes. How cool is that? Triangles really do help us in many ways!