Right triangle - ratio

The lengths of the legs of the right triangle ABC are in ratio b = 2:3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle.

Correct answer:

a =  5.547 cm
b =  8.3205 cm

Step-by-step explanation:

$$\begin{gathered} a:b=2:3 \\ b=3/2\cdot a \\ c=10\text{cm} \\ {c}^2=a^2+b^2 \\ {c}^2=a^2+(3/2a{)}^2 \\ {c}^2=a^2+(3/2{)}^2\cdot a^2 \\ a=\sqrt{\frac{c^2}{1+(3/2{)}^2}}=\sqrt{\frac{10^2}{1+(3/2{)}^2}}=5.547\text{cm} \end{gathered}$$

$b=3/2\cdot a=3/2\cdot 5.547=8.3205\text{cm}$

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