1. **Problem:** Solve for $x$ given the proportion $$\frac{6}{3} = \frac{x}{5}$$. 2. **Step 1:** Simplify the left side: $$\frac{6}{3} = 2$$. 3. **Step 2:** Set up the equation: $$2 = \frac{x}{5}$$. 4. **Step 3:** Multiply both sides by 5 to solve for $x$: $$x = 2 \times 5 = 10$$. 5. **Answer:** $x = 10$. 1. **Problem:** Given two similar triangles with sides 400 and 150 in one, and 120 and $x$ in the other, find $x$ using the proportion $$\frac{400}{150} = \frac{120}{x}$$. 2. **Step 1:** Cross multiply: $$400 \times x = 150 \times 120$$. 3. **Step 2:** Calculate the right side: $$150 \times 120 = 18000$$. 4. **Step 3:** Solve for $x$: $$400x = 18000 \Rightarrow x = \frac{18000}{400} = 45$$. 5. **Answer:** $x = 45$. 1. **Problem:** In a triangle with angles $3m$ and $4m$ and base 8 m, a segment parallel to the base divides the base into segments $x$ and $y$ with an internal segment of 5 m. 2. **Step 1:** Since the segment is parallel to the base, triangles are similar. 3. **Step 2:** Use similarity ratios to relate $x$, $y$, and 5 m. 4. **Step 3:** Without additional data, the problem is incomplete for numeric solution. 5. **Answer:** More information needed to solve for $x$ and $y$. 1. **Problem:** Right triangle with tree height 25 m, base 75 m, and vertical segment 12 m from base to hypotenuse; find height $x$. 2. **Step 1:** Use similar triangles formed by the vertical segment. 3. **Step 2:** Set up proportion: $$\frac{x}{12} = \frac{25}{75} = \frac{1}{3}$$. 4. **Step 3:** Solve for $x$: $$x = \frac{12}{3} = 4$$. 5. **Answer:** $x = 4$ meters. 1. **Problem:** Trapezoid-like shape with slant length 4.5, horizontal segments 3 and 2, and top horizontal segment $x$. 2. **Step 1:** Use Pythagoras theorem or segment addition to find $x$. 3. **Step 2:** Since the slant is 4.5 and horizontal segments are 3 and 2, total base is 5. 4. **Step 3:** Without vertical height or angles, $x$ cannot be determined numerically. 5. **Answer:** More information needed to solve for $x$. 1. **Problem:** No visible content for problem 6. 2. **Answer:** Cannot solve without problem details.