Perpendicular 40203

In a right triangle, one perpendicular is 5 cm longer than the other perpendicular. The diaphragm is 150 mm. Calculate the lengths of the hangings.

Correct answer:

a =  12.8078 cm
b =  7.8078 cm

Step-by-step explanation:

$$\begin{gathered} c=150\text{mm}\to \text{cm}=150:10\text{cm}=15\text{cm} \\ a=5+b \\ {a}^2+b^2=c^2 \\ {a}^2+(a-5{)}^2=c^2 \\ {a}^2+(a-5{)}^2=15^2 \\ 2a^2-10a-200=0 \\ 2...\text{ prime number} \\ 10=2\cdot 5 \\ 200=2^3\cdot 5^2 \\ \text{GCD}(2,10,200)=2 \\ {a}^2-5a-100=0 \\ p=1;q=-5;r=-100 \\ D=q^2-4pr=5^2-4\cdot 1\cdot (-100)=425 \\ D>0 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{5\pm \sqrt{425}}{2}=\frac{5\pm 5\sqrt{17}}{2} \\ {a}_{1,2}=2.5\pm 10.307764 \\ {a}_1=12.807764064 \\ {a}_2=-7.807764064 \\ a=a_1=12.8078=12.8078\text{cm} \end{gathered}$$

Our quadratic equation calculator calculates it.

$$\begin{gathered} b=a-5=12.8078-5\doteq 7.8078\text{cm} \\ \text{ Verifying Solution: } \\ {c}_1=a^2+b^2=12.8078^2+7.8078^2=225 \end{gathered}$$

Try another example