Answer: Length of one leg =x = 11.3 m
Length of another leg = 11.3-3 = 8.3 m
Step-by-step explanation:
Let one leg of the right triangle be x , then the other leg be x-3.
Hypotenuse = 14 meters
Then for the given situation , we have
[tex](14)^2=x^2+(x-3)^2\\\\\Rightarrow\ 196=x^2+x^2+3^2-2(3)x\\\\\Rightarrow\ 196=2x^2+9-6x\\\\\Rightarrow 2x^2+9-6x-196=0\\\\\Rightarrow 2x^2-6x-187[/tex]
Which is a quadratic equation.
For quadratic equation[tex]ax^2+bx+c[/tex], the root of equation is [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In [tex]2x^2-6x-187[/tex] , a= 2 , b= -6 and c=-187 , then
[tex]x=\dfrac{-(-6)\pm\sqrt{(-6)^2-4(2)(-187)}}{2(2)}[/tex]
[tex]x=\dfrac{6\pm\sqrt{1532}}{4}[/tex]
[tex]x\approx\dfrac{6\pm 39.14}{4}\\\\ x=\dfrac{6+39.14}{4}\ or\ x=\dfrac{6-39.14}{4}[/tex]
[tex]\\\\ x=11.285\ or\ x=-8.285[/tex]
Side cannot be negative , so avoid x=-8.285.
so [tex]x=11.285\approx11.3[/tex]
⇒ Length of one leg =x = 11.3 m
Length of another leg = 11.3-3 = 8.3 m
