One leg of a right triangle is 3 meters shorter than the other leg. If the hypotenuse is 14 meters, find the length of the two legs. Approximate your answers to the nearest tenth of a meter. Answer with the smaller of the legs first.

Answer: Length of one leg =x = 11.3 mLength of another leg = 11.3-3 = 8.3 mStep-by-step explanation:Let one leg of the right triangle be x , then the other leg be x-3.Hypotenuse = 14 metersPythagoras theorem of right -triangle says that he square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.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 mLength of another leg = 11.3-3 = 8.3 m