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  c2=a2+b2 o=a+b+c c2=a2+(o−a−c)2  302=a2+(42−a)2   −2a2+84a−864=0 2a2−84a+864=0  p=2;q=−84;r=864 D=q2−4pr=842−4⋅2⋅864=144 D>0  a1,2=−q±D2p=84±1444 a1,2=84±124 a1,2=21±3 a1=24 a2=18   Factored form of the equation:  2(a−24)(a−18)=0 a=a1=24=24  m 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 }

Checkout calculation with our calculator of quadratic equations.

b=a2  b=o−a−c=72−24−30=18=18  m b = a_{ 2 } \ \\ \ \\ b = o-a-c = 72-24-30 = 18 = 18 \ \text { m }

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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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