Right triangle

Legs of the right triangle are in the ratio a:b = 2:8. The hypotenuse has a length of 87 cm.

Calculate the perimeter and area of the triangle.

Correct result:

o =  192.503 cm
S =  890.4706 cm²

Solution:

$$\begin{gathered} c=87\text{ cm } \\ a:b=2:8 \\ {c}^2=a^2+b^2 \\ {c}^2=a^2+(8\mathrm{/}2\cdot a{)}^2 \\ {c}^2=a^2+(8\mathrm{/}2{)}^2{a}^2 \\ {c}^2=a^2(1+(8\mathrm{/}2{)}^2) \\ a=c\mathrm{/}\sqrt{1+(8\mathrm{/}2{)}^2}=87\mathrm{/}\sqrt{1+(8\mathrm{/}2{)}^2}\doteq 21.1006\text{ cm } \\ b=a\cdot {\displaystyle \frac{8}{2}}=21.1006\cdot {\displaystyle \frac{8}{2}}\doteq 84.4024\text{ cm } \\ o=a+b+c=21.1006+84.4024+87=192.503\text{ cm} \end{gathered}$$

$S={\displaystyle \frac{a\cdot b}{2}}={\displaystyle \frac{21.1006\cdot 84.4024}{2}}={\displaystyle \frac{15138}{17}}=890.4706{\text{cm}}^2$

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