Question

8)
find x if us = 2x - 7 an
medians.
(image of a triangle with side lengths 9x+1, 35, 16, 20 and an angle bisector or median?)

Explanation:

Step1: Identify the theorem (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, $\frac{9x + 1}{16}=\frac{35}{20}$.

Step2: Simplify the right - hand side

Simplify $\frac{35}{20}$ to $\frac{7}{4}$. So the equation becomes $\frac{9x + 1}{16}=\frac{7}{4}$.

Step3: Cross - multiply

Cross - multiplying gives $4(9x + 1)=16\times7$.

Step4: Expand and simplify

Expand the left - hand side: $36x+4 = 112$. Subtract 4 from both sides: $36x=112 - 4=108$.

Step5: Solve for x

Divide both sides by 36: $x=\frac{108}{36}=3$.

Answer:

$x = 3$