Question

Segment KJ shown below is the hypotenuse of isosceles right triangle JLK.



What is the length of one of the congruent legs of JLK?
3

6

Answer 1

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=$\sqrt{(2-2)^2+(-2-4)^2}$

JK=$6$

Now, it is given that Triangle JKL has congruent sides, thus let JL=LK=x, then using Pythagoras theorem, we have

$(JK)^{2}=(JL)^2+(LK)^2$

⇒$36=x^2+x^2$

⇒$36=2x^2$

⇒$x^2=18$

⇒$x=\sqrt{18}$

Thus, the length of one of the congruent legs of JLK is $\sqrt{18}$

Answer 2

The length of one of the congruent legs of JLK is $\sqrt{18$

From the figure, we have the following coordinates:

J(2,4), K(2,-2) and L(5,1).

The congruent sides of the triangle are: JL and LK

The length LK is calculated using the following distance formula

$LK =\sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}$

So, we have:

$LK =\sqrt{(5-2)^2 + (1 +2)^2}$

$LK =\sqrt{9+9}$

$LK =\sqrt{18}$

Hence, the length of one of the congruent legs of JLK is $\sqrt{18$

Read more about isosceles right triangles at:

https://brainly.com/question/1512106