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 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+87=192.503 cmc=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=a b2=21.1006 84.40242=1513817=890.471 cm2S=\dfrac{ a \cdot \ b }{ 2 }=\dfrac{ 21.1006 \cdot \ 84.4024 }{ 2 }=\dfrac{ 15138 }{ 17 }=890.471 \ \text{cm}^2

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