Answer:
Step-by-step explanation:
From the given figure, we get the coordinates of J,K and L as:
J(2,4), K(2,-2) and L(5,1).
Now, Using the distance formula,
JK=![\sqrt{(2-2)^2+(-2-4)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%282-2%29%5E2%2B%28-2-4%29%5E2%7D)
JK=![6](https://tex.z-dn.net/?f=6)
Now, it is given that Triangle JKL has congruent sides, thus let JL=LK=x, then using Pythagoras theorem, we have
![(JK)^{2}=(JL)^2+(LK)^2](https://tex.z-dn.net/?f=%28JK%29%5E%7B2%7D%3D%28JL%29%5E2%2B%28LK%29%5E2)
⇒![36=x^2+x^2](https://tex.z-dn.net/?f=36%3Dx%5E2%2Bx%5E2)
⇒![36=2x^2](https://tex.z-dn.net/?f=36%3D2x%5E2)
⇒![x^2=18](https://tex.z-dn.net/?f=x%5E2%3D18)
⇒![x=\sqrt{18}](https://tex.z-dn.net/?f=x%3D%5Csqrt%7B18%7D)
Thus, the length of one of the congruent legs of JLK is ![\sqrt{18}](https://tex.z-dn.net/?f=%5Csqrt%7B18%7D)