The right triangle

The right triangle ABC has a leg a = 36 cm and an area S = 540 cm². Calculate the length of the leg b and the median t2 to side b.

Correct answer:

b =  30 cm
t₂ =  39 cm

Step-by-step explanation:

$$\begin{gathered} a=36\text{ cm } \\ S=540{\text{cm}}^2 \\ S={\displaystyle \frac{ab}{2}} \\ b=2\cdot S\mathrm{/}a=2\cdot 540\mathrm{/}36=30\text{ cm} \end{gathered}$$

$$\begin{gathered} t_2^2=a^2+(b\mathrm{/}2{)}^2 \\ {t}_2=\sqrt{a^2+(b\mathrm{/}2{)}^2}=\sqrt{36^2+(30\mathrm{/}2{)}^2}=39\text{ cm} \end{gathered}$$

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