RT 11

Calculate the area of right tirangle if its perimeter is p = 45 m and one cathethus is 20 m long.

Correct answer:

S =  45 m²

Step-by-step explanation:

$$\begin{gathered} b=20 \\ {c}^2=a^2+b^2 \\ 45=a+b+c \\ S={\displaystyle \frac{1}{2}}ab \\ 45=a+b+\sqrt{a^2+b^2} \\ 45=a+20+\sqrt{a^2+20^2} \\ 25=a+\sqrt{a^2+400} \\ 25-a=\sqrt{a^2+400} \\ 625-50a+a^2=a^2+400 \\ 625-50a=400 \\ 625-400=50a \\ a=(625-400)\mathrm{/}50=4.5 \\ S={\displaystyle \frac{1}{2}}ab={\displaystyle \frac{1}{2}}\cdot 4.5\cdot 20=45{\text{m}}^2 \end{gathered}$$

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