Question

1. look at the figure. find jl

x + 5
2x - 7

Explanation:

Step1: Assume congruent right - triangles

Since the two right - triangles $\triangle{JKL}$ and $\triangle{MLK}$ share a common hypotenuse $JL = ML$ and right - angles $\angle{K}=\angle{M} = 90^{\circ}$, and we can assume they are congruent by Hypotenuse - Leg (HL) congruence criterion. So, $JK=ML$.

Step2: Set up the equation

Set up the equation based on the side - length expressions: $x + 5=2x−7$.

Step3: Solve the equation for $x$

Subtract $x$ from both sides: $5=2x - x-7$, which simplifies to $5=x - 7$. Then add 7 to both sides: $x=5 + 7=12$.

Step4: Find the length of $JK$

Substitute $x = 12$ into the expression for $JK$. $JK=x + 5=12+5 = 17$.

Answer:

17