Question

what is i? i =

Explanation:

Step1: Identify congruent triangles

Triangles $\triangle GJH$ and $\triangle IJH$ are congruent by the Hypotenuse - Leg (HL) congruence criterion since $\angle G=\angle I = 90^{\circ}$, $JH = JH$ (common side) and $\angle GHJ=\angle IHJ = 58^{\circ}$. So, $GJ=JI$.

Step2: Set up equation

Set up the equation $x + 8=3x$.

Step3: Solve for x

Subtract $x$ from both sides: $8 = 3x-x$, which simplifies to $8 = 2x$. Then divide both sides by 2: $x = 4$.

Step4: Find length of JI

Substitute $x = 4$ into the expression for $JI$ (which is $3x$). So, $JI=3\times4=12$.

Answer:

12