Question

In right ∆ ABC, the lengths of the legs are given. Find the length of the hypotenuse.
(i) a = 6 cm, b = 8 cm
(ii) a = 8 cm, b = 15 cm
(iii) a = 3 cm, b = 4 cm
(iv) a = 2 cm, b = 1.5 cm

Answer 1

According to the Pythagoras theorem,
$(\mathrm{Hypotenuse}{)}^2=(\mathrm{Base}{)}^2+(\mathrm{Height}{)}^2$

$$\begin{gathered} \left(\mathrm{i}\right){\mathrm{c}}^2={\mathrm{a}}^2+{\mathrm{b}}^2 \\ {\mathrm{c}}^2=6^2+8^2 \\ {\mathrm{c}}^2=36+64=100 \\ \mathrm{c}=10\mathrm{cm} \\ \left(\mathrm{ii}\right){\mathrm{c}}^2={\mathrm{a}}^2+{\mathrm{b}}^2 \\ {\mathrm{c}}^2=8^2+{15}^2 \\ {\mathrm{c}}^2=64+225=289 \\ \mathrm{c}=17\mathrm{cm} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{iii}\right){\mathrm{c}}^2={\mathrm{a}}^2+{\mathrm{b}}^2 \\ {\mathrm{c}}^2=3^2+4^2 \\ {\mathrm{c}}^2=9+16=25 \\ \mathrm{c}=5\mathrm{cm} \\ \left(\mathrm{iv}\right){\mathrm{c}}^2={\mathrm{a}}^2+{\mathrm{b}}^2 \\ {\mathrm{c}}^2=2^2+1.5^2 \\ {\mathrm{c}}^2=4+2.25=6.25 \\ \mathrm{c}=2.5\mathrm{cm} \end{gathered}$$