Hypotenuse 79904

I have a right triangle, the length of the hypotenuse is c 20, and I only know the side ratio a:b = 2:1. I can't figure out the actual length of the hangers = I'm already an old man, and my brain doesn't work at 100% like it did years ago at school - I could definitely do it back then...

Correct answer:

a =  17.8885 cm
b =  8.9443 cm

Step-by-step explanation:

$$\begin{gathered} c=20\text{cm} \\ a:b=2:1=2b:1b \\ {a}^2+b^2=c^2 \\ (2b{)}^2+(1b{)}^2=c^2 \\ 4b^2+b^2=c^2 \\ 5b^2=c^2 \\ b=c/\sqrt{5}=20/\sqrt{5}=4\sqrt{5}\text{cm}\doteq 8.9443\text{cm} \\ a=2\cdot b=2\cdot 8.9443=8\sqrt{5}\doteq 17.8885\text{cm} \\ \text{ Verifying Solution: } \\ r=a:b=17.8885:8.9443=2=2:1 \\ {c}_2=\sqrt{a^2+b^2}=\sqrt{17.8885^2+8.9443^2}=20 \end{gathered}$$

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