# 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:

$c = 87 \ cm \ \\ a:b = 2:8 \ \\ c^2 = a^2+b^2 \ \\ c^2 = a^2+(8/2 \cdot \ a)^2 \ \\ c^2 = a^2+(8/2)^2 \ a^2 \ \\ c^2 = a^2 (1 +(8/2)^2 ) \ \\ \ \\ a = c / \sqrt{ 1 +(8/2)^2 } = 87 / \sqrt{ 1 +(8/2)^2 } \doteq 21.1006 \ cm \ \\ \ \\ b = a \cdot \ \dfrac{ 8 }{ 2 } = 21.1006 \cdot \ \dfrac{ 8 }{ 2 } \doteq 84.4024 \ cm \ \\ \ \\ o = a+b+c = 21.1006+84.4024+87 \doteq 192.503 = 192.503 \ \text { cm }$
$S = \dfrac{ a \cdot \ b }{ 2 } = \dfrac{ 21.1006 \cdot \ 84.4024 }{ 2 } = \dfrac{ 15138 }{ 17 } \doteq 890.4706 = 890.471 \ cm^2$

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#### Following knowledge from mathematics are needed to solve this word math problem:

Looking for help with calculating roots of a quadratic equation? Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation? Pythagorean theorem is the base for the right triangle calculator. See also our trigonometric triangle calculator.

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