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.

Result

o =  192.503 cm
S =  890.471 cm2

Solution:

c=87 cm a:b=2:8 c2=a2+b2 c2=a2+(8/2 a)2 c2=a2+(8/2)2 a2 c2=a2(1+(8/2)2)  a=c/1+(8/2)2=87/1+(8/2)221.1006 cm  b=a 82=21.1006 8284.4024 cm  o=a+b+c=21.1006+84.4024+87192.503=192.503  cm c = 87 \ 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 \ cm \ \\ \ \\ b = a \cdot \ \dfrac{ 8 }{ 2 } = 21.1006 \cdot \ \dfrac{ 8 }{ 2 } \doteq 84.4024 \ cm \ \\ \ \\ o = a+b+c = 21.1006+84.4024+87 \doteq 192.503 = 192.503 \ \text{ cm }
S=a b2=21.1006 84.40242=1513817890.4706=890.471 cm2S = \dfrac{ a \cdot \ b }{ 2 } = \dfrac{ 21.1006 \cdot \ 84.4024 }{ 2 } = \dfrac{ 15138 }{ 17 } \doteq 890.4706 = 890.471 \ cm^2

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