Question

If the sides of a triangle measure 18 cm,18$\sqrt{3}$ and 36 cm, show that it is a 30$°$ -60$°$-90$°$ triangle.

Answer 1

Let Δ PQR be the triangle in which PQ = 18 cm, QR =18$\sqrt{3}$ cm and PR = 36 cm.
Then,

PQ : QR : PR = 18 : 18$\sqrt{3}$ : 36
= 1 : $\sqrt{3}$ : 2
= $\frac{1}{2}:\frac{\sqrt{3}}{2}:1$

Thus, PQ=$\frac{1}{2}$$\times$PR and QR=$\frac{\sqrt{3}}{2}$ $\times$ PR.

By the converse of 30°-60°-90° theorem, Δ PQR is a 30°-60°-90° triangle.