Desmos Graphing Calculator

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Math·Geometry and Trigonometry·Lines, angles, and triangles

hard

The line segment slants gradually up from left to right. The line segment begins at the point (negative 7 comma 4). The line segment ends at the point (5 comma 7). The line segment shown in the $xy$-plane represents side $JK$ of isosceles triangle $JKL$, where side $JL$ is congruent to side $KL$. The perimeter of this triangle is $13\sqrt{17}$ units. What is the length, in units, of side $JL$ of this triangle?

A

$\sqrt{17}$

B

$3\sqrt{17}$

C

$5\sqrt{17}$

D

$6\sqrt{17}$