# 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 =  890.471 cm2

#### Solution:

$c=87 \ \text{cm} \ \\ a:b=2:8 \ \\ c^2=a^2+b^2 \ \\ c^2=a^2+(8/2 \cdot \ a)^2 \ \\ c^2=a^2+(8/2)^2 \ a^2 \ \\ c^2=a^2 (1 +(8/2)^2 ) \ \\ \ \\ a=c / \sqrt{ 1 +(8/2)^2 }=87 / \sqrt{ 1 +(8/2)^2 } \doteq 21.1006 \ \text{cm} \ \\ \ \\ b=a \cdot \ \dfrac{ 8 }{ 2 }=21.1006 \cdot \ \dfrac{ 8 }{ 2 } \doteq 84.4024 \ \text{cm} \ \\ \ \\ o=a+b+c=21.1006+84.4024+87=192.503 \ \text{cm}$
$S=\dfrac{ a \cdot \ b }{ 2 }=\dfrac{ 21.1006 \cdot \ 84.4024 }{ 2 }=\dfrac{ 15138 }{ 17 }=890.471 \ \text{cm}^2$

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