Question

1. find y.

there is a triangle diagram with sides labeled: one side is y + 6, another side is 24, the base is divided into two segments: 2y - 4 and 40, and there is a segment from the vertex to the base (angle bisector or median - related).

Explanation:

Step1: Apply Angle Bisector Theorem

The Angle Bisector Theorem states that if a bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides. So, we have the proportion: $\frac{y + 6}{24}=\frac{2y - 4}{40}$

Step2: Cross - Multiply

Cross - multiplying gives us $40(y + 6)=24(2y - 4)$

Step3: Expand Both Sides

Expanding the left side: $40y+240$; expanding the right side: $48y - 96$
So, the equation becomes $40y + 240=48y-96$

Step4: Solve for y

Subtract $40y$ from both sides: $240 = 8y-96$
Add 96 to both sides: $336 = 8y$
Divide both sides by 8: $y=\frac{336}{8}=42$

Answer:

$y = 42$