Question

In a right triangle, two sides are $12$ cm and $9$ cm. Find the hypotenuse.

Answer 1

Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

Let $\mathrm{PQR}$ be the triangle with $\mathrm{PQ}=9\mathrm{cm},\mathrm{QR}=12\mathrm{cm}$

Then according to Pythagoras' Theorem;

$$\begin{gathered} \Rightarrow {\left(\mathrm{PR}\right)}^2={\left(\mathrm{PQ}\right)}^2+{\left(\mathrm{QR}\right)}^2 \\ \Rightarrow {\left(\mathrm{PR}\right)}^2={\left(12\right)}^2+{\left(9\right)}^2 \\ \Rightarrow {\left(\mathrm{PR}\right)}^2=144+81 \\ \Rightarrow {\left(\mathrm{PR}\right)}^2=225 \\ \Rightarrow \mathrm{PR}=\sqrt{225} \\ \therefore \mathrm{PR}=15 \end{gathered}$$

Hence, the hypotenuse is $15$ cm.