Land boundary

The land is a right triangle. Its hypotenuse is 30 meters long, and its circumference is 72 meters. What are the sizes of the remaining sides of the land boundary?

Correct answer:

a =  24 m
b =  18 m

Step-by-step explanation:

$$\begin{gathered} c=30\text{m} \\ o=72\text{m} \\ {c}^2=a^2+b^2 \\ o=a+b+c \\ {c}^2=a^2+(o-a-c{)}^2 \\ 30^2=a^2+(42-a{)}^2 \\ 30^2=a^2+(42-a{)}^2 \\ -2a^2+84a-864=0 \\ 2a^2-84a+864=0 \\ 2...\text{ prime number} \\ 84=2^2\cdot 3\cdot 7 \\ 864=2^5\cdot 3^3 \\ \text{GCD}(2,84,864)=2 \\ {a}^2-42a+432=0 \\ p=1;q=-42;r=432 \\ D=q^2-4pr=42^2-4\cdot 1\cdot 432=36 \\ D>0 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{42\pm \sqrt{36}}{2} \\ {a}_{1,2}=\frac{42\pm 6}{2} \\ {a}_{1,2}=21\pm 3 \\ {a}_1=24 \\ {a}_2=18 \\ a=a_1=24=24\text{m} \end{gathered}$$

Our quadratic equation calculator calculates it.

$$\begin{gathered} b=a_2 \\ b=o-a-c=72-24-30=18\text{m} \end{gathered}$$

Try calculation via our triangle calculator.

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