Perpendicular sides

In a right triangle, one perpendicular is 1 m shorter than the hypotenuse. The other perpendicular is 2 m shorter than the hypotenuse. Find the lengths of all sides of the triangle.

Final Answer:

a =  4 m
b =  3 m
c =  5 m

Step-by-step explanation:

$$\begin{gathered} a=c-1 \\ b=c-2 \\ {c}^2=a^2+b^2 \\ {c}^2=(c-1{)}^2+(c-2{)}^2 \\ -c^2+6c-5=0 \\ {c}^2-6c+5=0 \\ p=1;q=-6;r=5 \\ D=q^2-4pr=6^2-4\cdot 1\cdot 5=16 \\ D>0 \\ {c}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{6\pm \sqrt{16}}{2} \\ {c}_{1,2}=\frac{6\pm 4}{2} \\ {c}_{1,2}=3\pm 2 \\ {c}_1=5 \\ {c}_2=1 \\ c>2 \\ c=c_1=5\text{m} \\ a=c-1=5-1=4\text{m} \end{gathered}$$

Our quadratic equation calculator calculates it.

$b=c-2=5-2=3\text{m}$

$c=5=5\text{m}$

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