Question

find the value of y.
6y
2
4y+8
3
© angelina instein, 2023

Explanation:

Step1: Apply the basic proportionality theorem (Thales' theorem)

If a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides those sides proportionally. Here, we have \(\frac{6y}{2}=\frac{4y + 8}{3}\)

Step2: Cross - multiply

Cross - multiplying the equation \(\frac{6y}{2}=\frac{4y + 8}{3}\) gives \(6y\times3=2\times(4y + 8)\)

$$18y=8y + 16$$

Step3: Solve for \(y\)

Subtract \(8y\) from both sides: \(18y-8y=8y + 16-8y\)

$$10y=16$$

Divide both sides by \(10\): \(y=\frac{16}{10}=\frac{8}{5} = 1.6\)

Answer:

\(y = 1.6\)