# Land boundary

The land has the shape of a right triangle. The hypotenuse has a length of 30m. The circumference of the land is 72 meters. What is the length of the remaining sides of the land boundary?

Result

a =  24 m
b =  18 m

#### Solution:

$c = 30 \ m \ \\ o = 72 \ m \ \\ \ \\ c^2 = a^2+b^2 \ \\ o = a+b+c \ \\ c^2 = a^2 + (o-a-c)^2 \ \\ \ \\ 30^2 = a^2 + (42-a)^2 \ \\ \ \\ \ \\ -2a^2 +84a -864 = 0 \ \\ 2a^2 -84a +864 = 0 \ \\ \ \\ p = 2; q = -84; r = 864 \ \\ D = q^2 - 4pr = 84^2 - 4\cdot 2 \cdot 864 = 144 \ \\ D>0 \ \\ \ \\ a_{1,2} = \dfrac{ -q \pm \sqrt{ D } }{ 2p } = \dfrac{ 84 \pm \sqrt{ 144 } }{ 4 } \ \\ a_{1,2} = \dfrac{ 84 \pm 12 }{ 4 } \ \\ a_{1,2} = 21 \pm 3 \ \\ a_{1} = 24 \ \\ a_{2} = 18 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 2 (a -24) (a -18) = 0 \ \\ a = a_{ 1 } = 24 = 24 \ \text { m }$

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$b = a_{ 2 } \ \\ \ \\ b = o-a-c = 72-24-30 = 18 = 18 \ \text { m }$

Try calculation via our triangle calculator.

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

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. Do you want to convert length units? See also our trigonometric triangle calculator.

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