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:

$$\begin{gathered} c=150\text{mm}\to \text{cm}=150:10\text{cm}=15\text{cm} \\ a=5+b \\ {a}^2+b^2=c^2 \\ {a}^2+(a-5{)}^2=c^2 \\ {a}^2+(a-5{)}^2=15^2 \\ 2a^2-10a-200=0 \\ p=2;q=-10;r=-200 \\ D=q^2-4pr=10^2-4\cdot 2\cdot (-200)=1700 \\ D>0 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{10\pm \sqrt{1700}}{4}=\frac{10\pm 10\sqrt{17}}{4} \\ {a}_{1,2}=2.5\pm 10.307764064044 \\ {a}_1=12.807764064044 \\ {a}_2=-7.8077640640442 \\ \text{ Factored form of the equation: } \\ 2(a-12.807764064044)(a+7.8077640640442)=0 \\ a=a_1=12.8078=12.8078\text{cm} \end{gathered}$$

Our quadratic equation calculator calculates it.

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

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