Question

the two triangles are similar. find the values of the variable.
m =

Explanation:

Step1: Set up proportion for similar triangles

Since the triangles are similar, the corresponding sides are proportional. So, we have $\frac{15}{10}=\frac{m + 4}{m}$.

Step2: Cross - multiply

Cross - multiplying gives us $15m=10(m + 4)$.

Step3: Distribute on the right side

Distribute 10 on the right side: $15m = 10m+40$.

Step4: Subtract 10m from both sides

Subtract $10m$ from both sides: $15m-10m=10m + 40-10m$, which simplifies to $5m=40$.

Step5: Solve for m

Divide both sides by 5: $m=\frac{40}{5}=8$.

Answer:

8